Class 10 Exam > Class 10 Notes > Mathematics Class 10 (Maharashtra SSC Board) > Textbook: Linear Equations in Two Variables
Textbook: Linear Equations in Two Variables | Mathematics Class 10 (Maharashtra SSC Board) PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
1
· Methods of solving linear equations in two variables - graphical method,
Cramer’s method
· Equations that can be transformed in linear equation in two variables
· Application of simultaneous equations
Let’s recall.
Linear equation in two variables
An equation which contains two variables and the degree of each term
containing variable is one, is called a linear equation in two variables.
ax + by + c = 0 is the general form of a linear equation in two variables;
a, b, c are real numbers and a, b are not equal to zero at the same time.
Ex. 3x - 4y + 12 = 0 is the general form of equation 3x = 4y - 12
Activity : Complete the following table
No. Equation Is the equation a linear equation in 2
variables ?
1
4m + 3n = 12
Yes
2
3x
2
- 7y = 13
3
2 x - 5 y = 16
4
0x + 6y - 3 = 0
5
0.3x + 0y -36 = 0
6
45
4
xy
7
4xy - 5y - 8 = 0
1
Linear Equations in Two Variables
Let’s study.
Page 2
1
· Methods of solving linear equations in two variables - graphical method,
Cramer’s method
· Equations that can be transformed in linear equation in two variables
· Application of simultaneous equations
Let’s recall.
Linear equation in two variables
An equation which contains two variables and the degree of each term
containing variable is one, is called a linear equation in two variables.
ax + by + c = 0 is the general form of a linear equation in two variables;
a, b, c are real numbers and a, b are not equal to zero at the same time.
Ex. 3x - 4y + 12 = 0 is the general form of equation 3x = 4y - 12
Activity : Complete the following table
No. Equation Is the equation a linear equation in 2
variables ?
1
4m + 3n = 12
Yes
2
3x
2
- 7y = 13
3
2 x - 5 y = 16
4
0x + 6y - 3 = 0
5
0.3x + 0y -36 = 0
6
45
4
xy
7
4xy - 5y - 8 = 0
1
Linear Equations in Two Variables
Let’s study.
2
Simultaneous linear equations
When we think about two linear equations in two variables at the same
time, they are called simultaneous equations.
Last year we learnt to solve simultaneous equations by eliminating one
variable. Let us revise it.
Ex. (1) Solve the following simultaneous equations.
(1) 5x - 3y = 8; 3x + y = 2
Solution :
Method I : 5x - 3y = 8. . . (I)
3x + y = 2 . . . (II)
Multiplying both sides of
equation (II) by 3.
9x + 3y = 6 . . . (III)
5x - 3y = 8. . . (I)
Now let us add equations (I)
and (III)
5x - 3y = 8
9x + 3y = 6
14x = 14
\ x = 1
substituting x = 1 in equation (II)
3x + y = 2
\ 3 ´ 1 + y = 2
\ 3 + y = 2
\ y = -1
solution is x = 1, y = -1; it is also
written as (x, y) = (1, -1)
Method (II)
5x - 3y = 8. . . (I)
3x + y = 2 . . . (II)
Let us write value of y in terms
of x from equation (II) as
y = 2 - 3x . . . (III)
Substituting this value of y in
equation (I).
5x - 3y = 8
\ 5x - 3(2 - 3x) = 8
\ 5x - 6 + 9x = 8
\ 14x - 6 = 8
\ 14x = 8 + 6
\ 14x = 14
\ x = 1
Substituting x = 1 in equation
(III).
y = 2 - 3x
\ y = 2 - 3 ´ 1
\ y = 2 - 3
\ y = -1
x = 1, y = -1 is the solution.
+
Page 3
1
· Methods of solving linear equations in two variables - graphical method,
Cramer’s method
· Equations that can be transformed in linear equation in two variables
· Application of simultaneous equations
Let’s recall.
Linear equation in two variables
An equation which contains two variables and the degree of each term
containing variable is one, is called a linear equation in two variables.
ax + by + c = 0 is the general form of a linear equation in two variables;
a, b, c are real numbers and a, b are not equal to zero at the same time.
Ex. 3x - 4y + 12 = 0 is the general form of equation 3x = 4y - 12
Activity : Complete the following table
No. Equation Is the equation a linear equation in 2
variables ?
1
4m + 3n = 12
Yes
2
3x
2
- 7y = 13
3
2 x - 5 y = 16
4
0x + 6y - 3 = 0
5
0.3x + 0y -36 = 0
6
45
4
xy
7
4xy - 5y - 8 = 0
1
Linear Equations in Two Variables
Let’s study.
2
Simultaneous linear equations
When we think about two linear equations in two variables at the same
time, they are called simultaneous equations.
Last year we learnt to solve simultaneous equations by eliminating one
variable. Let us revise it.
Ex. (1) Solve the following simultaneous equations.
(1) 5x - 3y = 8; 3x + y = 2
Solution :
Method I : 5x - 3y = 8. . . (I)
3x + y = 2 . . . (II)
Multiplying both sides of
equation (II) by 3.
9x + 3y = 6 . . . (III)
5x - 3y = 8. . . (I)
Now let us add equations (I)
and (III)
5x - 3y = 8
9x + 3y = 6
14x = 14
\ x = 1
substituting x = 1 in equation (II)
3x + y = 2
\ 3 ´ 1 + y = 2
\ 3 + y = 2
\ y = -1
solution is x = 1, y = -1; it is also
written as (x, y) = (1, -1)
Method (II)
5x - 3y = 8. . . (I)
3x + y = 2 . . . (II)
Let us write value of y in terms
of x from equation (II) as
y = 2 - 3x . . . (III)
Substituting this value of y in
equation (I).
5x - 3y = 8
\ 5x - 3(2 - 3x) = 8
\ 5x - 6 + 9x = 8
\ 14x - 6 = 8
\ 14x = 8 + 6
\ 14x = 14
\ x = 1
Substituting x = 1 in equation
(III).
y = 2 - 3x
\ y = 2 - 3 ´ 1
\ y = 2 - 3
\ y = -1
x = 1, y = -1 is the solution.
+
3
Ex. (2) Solve : 3x + 2y = 29; 5x - y = 18
Solution : 3x + 2y = 29. . . (I) and 5x - y = 18 . . . (II)
Let’s solve the equations by eliminating ’y’. Fill suitably the boxes below.
Multiplying equation (II) by 2.
\ 5x ´ - y ´ = 18 ´
\ 10x - 2y = . . . (III)
Let’s add equations (I) and (III)
3x + 2y = 29
+
- =
= \ x =
Substituting x = 5 in equation (I)
3x + 2y = 29
\ 3 ´ + 2y = 29
\ + 2y = 29
\ 2y = 29 -
\ 2y = \ y =
(x, y) = ( , ) is the solution.
Ex. (3) Solve : 15x + 17y = 21; 17x + 15y = 11
Solution : 15x + 17y = 21. . . (I)
17x + 15y = 11 . . . (II)
In the two equations above, the coefficients of x and y are interchanged.
While solving such equations we get two simple equations by adding and
subtracting the given equations. After solving these equations, we can easily find
the solution.
Let’s add the two given equations.
15x + 17y = 21
17x + 15y = 11
32x + 32y = 32
+
Page 4
1
· Methods of solving linear equations in two variables - graphical method,
Cramer’s method
· Equations that can be transformed in linear equation in two variables
· Application of simultaneous equations
Let’s recall.
Linear equation in two variables
An equation which contains two variables and the degree of each term
containing variable is one, is called a linear equation in two variables.
ax + by + c = 0 is the general form of a linear equation in two variables;
a, b, c are real numbers and a, b are not equal to zero at the same time.
Ex. 3x - 4y + 12 = 0 is the general form of equation 3x = 4y - 12
Activity : Complete the following table
No. Equation Is the equation a linear equation in 2
variables ?
1
4m + 3n = 12
Yes
2
3x
2
- 7y = 13
3
2 x - 5 y = 16
4
0x + 6y - 3 = 0
5
0.3x + 0y -36 = 0
6
45
4
xy
7
4xy - 5y - 8 = 0
1
Linear Equations in Two Variables
Let’s study.
2
Simultaneous linear equations
When we think about two linear equations in two variables at the same
time, they are called simultaneous equations.
Last year we learnt to solve simultaneous equations by eliminating one
variable. Let us revise it.
Ex. (1) Solve the following simultaneous equations.
(1) 5x - 3y = 8; 3x + y = 2
Solution :
Method I : 5x - 3y = 8. . . (I)
3x + y = 2 . . . (II)
Multiplying both sides of
equation (II) by 3.
9x + 3y = 6 . . . (III)
5x - 3y = 8. . . (I)
Now let us add equations (I)
and (III)
5x - 3y = 8
9x + 3y = 6
14x = 14
\ x = 1
substituting x = 1 in equation (II)
3x + y = 2
\ 3 ´ 1 + y = 2
\ 3 + y = 2
\ y = -1
solution is x = 1, y = -1; it is also
written as (x, y) = (1, -1)
Method (II)
5x - 3y = 8. . . (I)
3x + y = 2 . . . (II)
Let us write value of y in terms
of x from equation (II) as
y = 2 - 3x . . . (III)
Substituting this value of y in
equation (I).
5x - 3y = 8
\ 5x - 3(2 - 3x) = 8
\ 5x - 6 + 9x = 8
\ 14x - 6 = 8
\ 14x = 8 + 6
\ 14x = 14
\ x = 1
Substituting x = 1 in equation
(III).
y = 2 - 3x
\ y = 2 - 3 ´ 1
\ y = 2 - 3
\ y = -1
x = 1, y = -1 is the solution.
+
3
Ex. (2) Solve : 3x + 2y = 29; 5x - y = 18
Solution : 3x + 2y = 29. . . (I) and 5x - y = 18 . . . (II)
Let’s solve the equations by eliminating ’y’. Fill suitably the boxes below.
Multiplying equation (II) by 2.
\ 5x ´ - y ´ = 18 ´
\ 10x - 2y = . . . (III)
Let’s add equations (I) and (III)
3x + 2y = 29
+
- =
= \ x =
Substituting x = 5 in equation (I)
3x + 2y = 29
\ 3 ´ + 2y = 29
\ + 2y = 29
\ 2y = 29 -
\ 2y = \ y =
(x, y) = ( , ) is the solution.
Ex. (3) Solve : 15x + 17y = 21; 17x + 15y = 11
Solution : 15x + 17y = 21. . . (I)
17x + 15y = 11 . . . (II)
In the two equations above, the coefficients of x and y are interchanged.
While solving such equations we get two simple equations by adding and
subtracting the given equations. After solving these equations, we can easily find
the solution.
Let’s add the two given equations.
15x + 17y = 21
17x + 15y = 11
32x + 32y = 32
+
4
Dividing both sides of the equation by 32.
x + y = 1 . . . (III)
Now, let’s subtract equation (II) from (I)
15x + 17y = 21
17x + 15y = 11
-2x + 2y = 10
dividing the equation by 2.
-x + y = 5 . . . (IV)
Now let’s add equations (III) and (V).
x + y = 1
-x + y = 5
\ 2y = 6 \ y = 3
Place this value in equation (III).
x + y = 1
\ x + 3 = 1
\ x = 1 - 3 \ x = -2
(x, y) = (-2, 3) is the solution.
- - -
Practice Set 1.1
(1) Complete the following activity to solve the simultaneous equations.
5x + 3y = 9 -----(I)
-
+
+
2x - 3y = 12 ----- (II)
Let’s add eqations (I) and (II).
5x + 3y = 9
2x - 3y = 12
x =
x = x =
Place x = 3 in equation (I).
5 ´ + 3y = 9
3y = 9 -
3y =
y =
3
y =
\ Solution is (x, y) = ( , ).
Page 5
1
· Methods of solving linear equations in two variables - graphical method,
Cramer’s method
· Equations that can be transformed in linear equation in two variables
· Application of simultaneous equations
Let’s recall.
Linear equation in two variables
An equation which contains two variables and the degree of each term
containing variable is one, is called a linear equation in two variables.
ax + by + c = 0 is the general form of a linear equation in two variables;
a, b, c are real numbers and a, b are not equal to zero at the same time.
Ex. 3x - 4y + 12 = 0 is the general form of equation 3x = 4y - 12
Activity : Complete the following table
No. Equation Is the equation a linear equation in 2
variables ?
1
4m + 3n = 12
Yes
2
3x
2
- 7y = 13
3
2 x - 5 y = 16
4
0x + 6y - 3 = 0
5
0.3x + 0y -36 = 0
6
45
4
xy
7
4xy - 5y - 8 = 0
1
Linear Equations in Two Variables
Let’s study.
2
Simultaneous linear equations
When we think about two linear equations in two variables at the same
time, they are called simultaneous equations.
Last year we learnt to solve simultaneous equations by eliminating one
variable. Let us revise it.
Ex. (1) Solve the following simultaneous equations.
(1) 5x - 3y = 8; 3x + y = 2
Solution :
Method I : 5x - 3y = 8. . . (I)
3x + y = 2 . . . (II)
Multiplying both sides of
equation (II) by 3.
9x + 3y = 6 . . . (III)
5x - 3y = 8. . . (I)
Now let us add equations (I)
and (III)
5x - 3y = 8
9x + 3y = 6
14x = 14
\ x = 1
substituting x = 1 in equation (II)
3x + y = 2
\ 3 ´ 1 + y = 2
\ 3 + y = 2
\ y = -1
solution is x = 1, y = -1; it is also
written as (x, y) = (1, -1)
Method (II)
5x - 3y = 8. . . (I)
3x + y = 2 . . . (II)
Let us write value of y in terms
of x from equation (II) as
y = 2 - 3x . . . (III)
Substituting this value of y in
equation (I).
5x - 3y = 8
\ 5x - 3(2 - 3x) = 8
\ 5x - 6 + 9x = 8
\ 14x - 6 = 8
\ 14x = 8 + 6
\ 14x = 14
\ x = 1
Substituting x = 1 in equation
(III).
y = 2 - 3x
\ y = 2 - 3 ´ 1
\ y = 2 - 3
\ y = -1
x = 1, y = -1 is the solution.
+
3
Ex. (2) Solve : 3x + 2y = 29; 5x - y = 18
Solution : 3x + 2y = 29. . . (I) and 5x - y = 18 . . . (II)
Let’s solve the equations by eliminating ’y’. Fill suitably the boxes below.
Multiplying equation (II) by 2.
\ 5x ´ - y ´ = 18 ´
\ 10x - 2y = . . . (III)
Let’s add equations (I) and (III)
3x + 2y = 29
+
- =
= \ x =
Substituting x = 5 in equation (I)
3x + 2y = 29
\ 3 ´ + 2y = 29
\ + 2y = 29
\ 2y = 29 -
\ 2y = \ y =
(x, y) = ( , ) is the solution.
Ex. (3) Solve : 15x + 17y = 21; 17x + 15y = 11
Solution : 15x + 17y = 21. . . (I)
17x + 15y = 11 . . . (II)
In the two equations above, the coefficients of x and y are interchanged.
While solving such equations we get two simple equations by adding and
subtracting the given equations. After solving these equations, we can easily find
the solution.
Let’s add the two given equations.
15x + 17y = 21
17x + 15y = 11
32x + 32y = 32
+
4
Dividing both sides of the equation by 32.
x + y = 1 . . . (III)
Now, let’s subtract equation (II) from (I)
15x + 17y = 21
17x + 15y = 11
-2x + 2y = 10
dividing the equation by 2.
-x + y = 5 . . . (IV)
Now let’s add equations (III) and (V).
x + y = 1
-x + y = 5
\ 2y = 6 \ y = 3
Place this value in equation (III).
x + y = 1
\ x + 3 = 1
\ x = 1 - 3 \ x = -2
(x, y) = (-2, 3) is the solution.
- - -
Practice Set 1.1
(1) Complete the following activity to solve the simultaneous equations.
5x + 3y = 9 -----(I)
-
+
+
2x - 3y = 12 ----- (II)
Let’s add eqations (I) and (II).
5x + 3y = 9
2x - 3y = 12
x =
x = x =
Place x = 3 in equation (I).
5 ´ + 3y = 9
3y = 9 -
3y =
y =
3
y =
\ Solution is (x, y) = ( , ).
5
2. Solve the following simultaneous equations.
(1) 3a + 5b = 26; a + 5b = 22 (2) x + 7y = 10; 3x - 2y = 7
(3) 2x - 3y = 9; 2x + y = 13 (4) 5m - 3n = 19; m - 6n = -7
(5) 5x + 2y = -3; x + 5y = 4 (6)
1
3
10
3
xy ;
2
1
4
11
4
xy
(7) 99x + 101y = 499; 101x + 99y = 501
(8) 49x - 57y = 172; 57x - 49y = 252
Let’s recall.
Graph of a linear equation in two variables
In the 9
th
standard we learnt that the graph of a linear equation in two
variables is a straight line. The ordered pair which satisfies the equation is a
solution of that equation. The ordered pair represents a point on that line.
Ex. Draw graph of 2x - y = 4.
Solution : To draw a graph of the equation let’s write 4 ordered pairs.
x 0 2 3 -1
y -4 0 2 -6
(x, y) (0, -4) (2, 0) (3, 2) (-1, -6)
To obtain ordered pair by
simple way let’s take x = 0
and then y = 0.
Scale : on both axes
1 cm = 1 unit.
-1 1
1
2
2
3 4 5 6 7 8 9
0
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
(3, 2)
(2, 0)
(0, -4)
(-1, -6)
X
X'
Y
Y'
Read More
|
26 videos|208 docs|38 tests
|
FAQs on Textbook: Linear Equations in Two Variables - Mathematics Class 10 (Maharashtra SSC Board)
| 1. What are linear equations in two variables and how can they be represented graphically? |  |
Ans. Linear equations in two variables are mathematical expressions that can be written in the form ax + by + c = 0, where a, b, and c are constants, and x and y are variables. Graphically, these equations represent straight lines on a Cartesian plane. The solutions of these equations correspond to the points where the line intersects the axes or any point on the line itself.
| 2. How do you find the solution of a linear equation in two variables? | |
Ans. To find the solution of a linear equation in two variables, you can use methods such as substitution, elimination, or graphical representation. In substitution, you solve one variable in terms of the other and substitute it back into the original equation. In elimination, you add or subtract equations to eliminate one variable. Graphically, you can plot the equation and identify the points that satisfy it.
| 3. What is the significance of the slope and intercept in the context of linear equations? | |
Ans. The slope of a linear equation indicates the steepness or incline of the line, reflecting how much y changes for a unit change in x. The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero. Together, the slope and intercept provide critical information about the line's characteristics and help in sketching the graph of the equation.
| 4. Can a linear equation in two variables have more than one solution? | |
Ans. Yes, a linear equation in two variables can have infinitely many solutions. This occurs because the equation represents a line on the Cartesian plane, and every point (x, y) on that line is a solution. However, there can also be cases where the line does not intersect with another line representing a different equation, leading to no solutions, or they intersect at a single point, leading to one solution.
| 5. How can we use linear equations in real-life situations? | |
Ans. Linear equations in two variables can be applied in various real-life scenarios, such as calculating costs, predicting trends, and solving problems involving relationships between two quantities. For example, they can be used in business to determine profit and loss scenarios, in science to analyze relationships between variables, or in everyday calculations like budgeting or planning trips based on distance and time.
About this Document
4.92/5
Rating
Sep 23, 2025
Last updated
Related Exams
Document Description: Textbook: Linear Equations in Two Variables for Class 10 2025 is part of Mathematics Class 10 (Maharashtra SSC Board) preparation.
The notes and questions for Textbook: Linear Equations in Two Variables have been prepared according to the Class 10 exam syllabus. Information about Textbook: Linear Equations in Two Variables covers topics
like and Textbook: Linear Equations in Two Variables Example, for Class 10 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Textbook: Linear Equations in Two Variables.
Introduction of Textbook: Linear Equations in Two Variables in English is available as part of our Mathematics Class 10 (Maharashtra SSC Board)
for Class 10 & Textbook: Linear Equations in Two Variables in Hindi for Mathematics Class 10 (Maharashtra SSC Board) course.
Download more important topics related with notes, lectures and mock test series for Class 10
Exam by signing up for free. Class 10: Textbook: Linear Equations in Two Variables | Mathematics Class 10 (Maharashtra SSC Board)
Description
Full syllabus notes, lecture & questions for Textbook: Linear Equations in Two Variables | Mathematics Class 10 (Maharashtra SSC Board) - Class 10 | Plus excerises question with solution to help you revise complete syllabus for Mathematics Class 10 (Maharashtra SSC Board) | Best notes, free PDF download
Information about Textbook: Linear Equations in Two Variables
In this doc you can find the meaning of Textbook: Linear Equations in Two Variables defined & explained in the simplest way possible. Besides explaining types of
Textbook: Linear Equations in Two Variables theory, EduRev gives you an ample number of questions to practice Textbook: Linear Equations in Two Variables tests, examples and also practice Class 10
tests
Related Searches
Textbook: Linear Equations in Two Variables | Mathematics Class 10 (Maharashtra SSC Board)
,Textbook: Linear Equations in Two Variables | Mathematics Class 10 (Maharashtra SSC Board)
,ppt
,study material
,Summary
,video lectures
,Textbook: Linear Equations in Two Variables | Mathematics Class 10 (Maharashtra SSC Board)
,Viva Questions
,shortcuts and tricks
,MCQs
,practice quizzes
,Semester Notes
,Free
,Previous Year Questions with Solutions
,past year papers
,Important questions
,Sample Paper
,Exam
,Extra Questions
,mock tests for examination
,Objective type Questions
;
Additional Information about Textbook: Linear Equations in Two Variables for Class 10 Preparation
Textbook: Linear Equations in Two Variables Free PDF Download
The Textbook: Linear Equations in Two Variables is an invaluable resource that delves deep into the core of the Class 10 exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Textbook: Linear Equations in Two Variables now and kickstart your journey towards success in the Class 10 exam.
Importance of Textbook: Linear Equations in Two Variables
The importance of Textbook: Linear Equations in Two Variables cannot be overstated, especially for Class 10 aspirants.
This document holds the key to success in the Class 10 exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Textbook: Linear Equations in Two Variables Notes
Textbook: Linear Equations in Two Variables Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Textbook: Linear Equations in Two Variables.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Textbook: Linear Equations in Two Variables Notes on EduRev are your ultimate resource for success.
Textbook: Linear Equations in Two Variables Class 10 Questions
The "Textbook: Linear Equations in Two Variables Class 10 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 10 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Textbook: Linear Equations in Two Variables on the App
Students of Class 10 can study Textbook: Linear Equations in Two Variables alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Textbook: Linear Equations in Two Variables,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Textbook: Linear Equations in Two Variables is prepared as per the latest Class 10 syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup