Practice Questions on Linear Equations

A linear equation is an equation in which each variable has a power of 1 and the graph of the equation is a straight line.

Solved Examples

Example 1: Solve 2x  = 3(x + 4)

Solution:

Given equation,

2x  = 3(x  + 4)
⇒ 2x = 3x + 3(4)
⇒ 2x = 3x + 12
⇒ 2x - 3x = 12
⇒ -x = 12
⇒ x = -12

Example 2: Solve 2x – y = 4 and x + y = 5

Solution: 

Given Equation,

• 2x – y = 4...(i)
• x + y = 5...(ii)

From eq. (ii) y = 5 - x

Putting the value of y from eq (ii) in eq (i) we get
2x + (5 - x) = 4
⇒ 2x + 5 - x = 4
⇒ 2x - x = 4 - 5
⇒ x = -1

Putting value of x in eq (i)
2(-1) - y = 4
⇒ -2 - y = 4
⇒ y = -2 - 4
⇒ y = -6

Thus,

• x = -1
• y = -6

Example 3: Solve 2x + 3y = 6 and x - y = 3.

Solution: 

Given Equation,

• 2x + 3y = 6 . . .(i)
• x - y = 3  . . .(ii)

take equation (ii), 

x = y + 3 . . .(iii)

putting the value of x from eq (iii) in eq (i) we get

2(y + 3) + 3y = 6
⇒ 2y + 6 + 3y = 6
⇒ 5y = 6 - 6
⇒ 5y = 0
⇒ y = 0

Putting the value of y in eq (iii)

x = y + 3 = 0 + 3 = 3

• x = 3
• y = 0

Practice Questions

Question 1: Solve the linear equation: 3x + 7 = 19.

Question 2: Find the value of y in the equation: 2y - 5 = 3y + 8.

Question 3: If the sum of two numbers is 15, and one of the numbers is 7, form a linear equation and find the other number.

Question 4: Solve for x in the equation: \frac{2x}{3} + 4 = 10.

Question 5: A mobile phone plan costs a fixed monthly charge of $30 plus $0.10 per minute of usage. If a user has a bill of $50, how many minutes did they use? Form and solve the linear equation.