Question

Solve the following system of equations by the elimination method:

5x + 8y = 44, 3x + 5y = 27

Answer 1

Given system of equations:

5x + 8y = 44   ...(i)

3x + 5y = 27   ...(ii)

Step 1: Make the coefficients of one variable equal

Multiply equation (i) by 3 and equation (ii) by 5 to get the coefficients of (x) equal:

3 × (5x + 8y) = 3 × 44 

⇒ 15x + 24y = 132   ...(iii) 

5 × (3x + 5y) = 5 × 27 

⇒ 15x + 25y = 135   ...(iv)

Step 2: Subtract equations (iii) from (iv) to eliminate (x)

(15x + 25y) – (15x + 24y) = 135 – 132 

15x – 15x + 25y – 24y = 3 

y = 3

Step 3: Substitute (y = 3) into one of the original equations, say (ii):

3x + 5(3) = 27

3x + 15 = 27

3x = 12

x = 4