Test: Substitution Method - Class 10 MCQ

# Test: Substitution Method - Class 10 MCQ

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## 10 Questions MCQ Test Mathematics (Maths) Class 10 - Test: Substitution Method

Test: Substitution Method for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The Test: Substitution Method questions and answers have been prepared according to the Class 10 exam syllabus.The Test: Substitution Method MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Substitution Method below.
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Test: Substitution Method - Question 1

### Find the solution to the following system of linear equations:  0.2x + 0.3y = 1.2 0.1x – 0.1y = 0.1​

Detailed Solution for Test: Substitution Method - Question 1

0.2x + 0.3y = 1.2
2x+3y=12   …..(1)
0.1x – 0.1y = 0.1​x-y=1  ….(2)
From (2), x=1+y
Substituting the values of x in (1)
2(1+y)+3y=12
2+2y+3y=12
5y=10
y=2
x=1+2= 3

Test: Substitution Method - Question 2

### Find the solution to the following system of linear equations: 3x-y+9=0 3x+4y-6 = 0​

Detailed Solution for Test: Substitution Method - Question 2

3x-y+9=0 …(1)
3x+4y-6=0  …(2)​
From 1
3x=y-9
Substituting in 2
y-9+4y-6=0
5y-15=0
y=3
x=-2

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Test: Substitution Method - Question 3

### Find the solution to the following system of linear equations:  2x-y+6=0 4x+5y-16 = 0​

Detailed Solution for Test: Substitution Method - Question 3

2x-y+6=0
y=2x+6   ….(1)
4x+5y-16=0​
Substituting the values
4x+5(2x+6)-16=0
14x+14=0
x=-1
y=4

Test: Substitution Method - Question 4

Find the solution to the following system of linear equations:
2p+3q = 9
p – q = 2​

Detailed Solution for Test: Substitution Method - Question 4

Alright, we have a system of two linear equations with two variables, p and q. Let's write them down:

1) 2p + 3q = 9
2) p - q = 2

Our goal is to find the values of p and q that satisfy both equations. We can use either the substitution method or the elimination method to solve this system. I'll use the substitution method here.

First, we'll solve the second equation for one of the variables. Let's solve for p:

p = q + 2

Now, we'll substitute this expression for p into the first equation:

2(q + 2) + 3q = 9

Distribute the 2:

2q + 4 + 3q = 9

Combine like terms:

5q + 4 = 9

Now, solve for q:

5q = 9 - 4
5q = 5
q = 1

Now that we have the value for q, we can plug it back into the expression for p:

p = q + 2
p = 1 + 2
p = 3

Test: Substitution Method - Question 5

Find the solution to the following system of linear equations:
2x-5y+4 = 0 2x+y-8 = 0​

Detailed Solution for Test: Substitution Method - Question 5

2x-5y+4=0…(I)

2x+y-8=0…(II)

From the equation II we get,

y=-2x+8

Substituting this value of y in equation II we get,

2x-5(-2x+8)+4=0

⇒12x -36=0

⇒x=3

Substituting this value of x in equation II we get,

y=2

Hence the solution is (3, 2).

Test: Substitution Method - Question 6

The sum of two numbers is 45 and one is twice the other. What is the smaller number?​

Detailed Solution for Test: Substitution Method - Question 6

Solution:

- Let's assume the smaller number is x.
- According to the given condition, the larger number is twice the smaller number, so it can be expressed as 2x.
- The sum of the two numbers is 45, so we can write the equation as: x + 2x = 45
- Combining like terms, we get 3x = 45
- Dividing both sides by 3, we find x = 15

Therefore, the smaller number is 15. So, the correct answer is C: 15.

Test: Substitution Method - Question 7

Find the solution to the following system of linear equations:
x-2y = 6
2x+y = 17​

Detailed Solution for Test: Substitution Method - Question 7

x-2y = 6

2x+y = 17​

2x - 4y = 12

2x + y  = 17

-5y   =   -5

y  =  1

x-2(1) = 6

x= 8

Test: Substitution Method - Question 8

The present age of a father is the sum of the ages of his three sons. Ten years from now his age will be a three quarter of the sum of their ages then. How old is the father?

Detailed Solution for Test: Substitution Method - Question 8

Test: Substitution Method - Question 9

Which of the following points lie on the line  3x+2y = 5 ?

Detailed Solution for Test: Substitution Method - Question 9

When we are given only one equation and two variables we assume values for one variable and find the values for the other variable.
3x+2y=5
Let x=1
3*1+2y=5
2y=2
y=1 hence (1,1) lies on the line.

Test: Substitution Method - Question 10

The Index of Coincidence for English language is approximately

## Mathematics (Maths) Class 10

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## Mathematics (Maths) Class 10

126 videos|477 docs|105 tests