Class 10 Exam > Class 10 Notes > Exercise 2 - Pair of Linear Equations in Two Variables, Class 10, Maths
Exercise 2 - Pair of Linear Equations in Two Variables, Class 10, Maths PDF Download
Pair of Linear Equations in Two Variables
Exercise 2
Question: 1. Form the pair of linear equations in the following problems, and find their solutions graphically.
(i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
(ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.
Question: 4. Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:
(i) x + y = 5, 2x + 2y = 10
(ii) x – y = 8, 3x – 3y = 16
(iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0
(iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0
Question: 5. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
6. Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) intersecting lines (ii) parallel lines (iii) coincident lines
FAQs on Exercise 2 - Pair of Linear Equations in Two Variables, Class 10, Maths
| 1. What is a pair of linear equations in two variables? |  |
Ans. A pair of linear equations in two variables is a set of two equations that involve two variables and their coefficients are all linear. These equations can be represented in the form ax + by = c, where a, b, and c are constants.
| 2. How do you solve a pair of linear equations in two variables? | |
Ans. To solve a pair of linear equations in two variables, we can use various methods such as substitution method, elimination method, and graphical method. These methods involve manipulating the equations to find the values of the variables that satisfy both equations simultaneously.
| 3. What is the substitution method for solving a pair of linear equations? | |
Ans. The substitution method involves solving one equation for one variable and substituting this value into the other equation. By substituting the known value, we can then solve for the other variable. This method allows us to find the values of both variables that satisfy the given pair of linear equations.
| 4. What is the elimination method for solving a pair of linear equations? | |
Ans. The elimination method involves adding or subtracting the equations in such a way that one of the variables gets eliminated. This results in a new equation with only one variable, which can be easily solved to find its value. By substituting this value back into one of the original equations, we can then find the value of the other variable.
| 5. How can we graphically solve a pair of linear equations in two variables? | |
Ans. To graphically solve a pair of linear equations, we plot the given equations on a coordinate plane. The point of intersection of the two lines represents the solution to the equations. By visually analyzing the graph, we can determine the coordinates of the intersection point and hence find the values of the variables that satisfy the given equations.
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