Question

Solve the following system of equations by the elimination method:

2(x + 1) + 3(y – 2) = 19, 3(x + 2) + 2(y – 1) = 26

Answer 1

Given system of equations:

2(x + 1) + 3(y – 2) = 19

3(x + 2) + 2(y – 1) = 26

Step 1: Expand both equations 

2x + 2 + 3y – 6 = 19 

3x + 6 + 2y – 2 = 26

Simplify:

2x + 3y – 4 = 19

⇒ 2x + 3y = 23

3x + 2y + 4 = 26

⇒ 3x + 2y = 22

Step 2: Multiply equations to align coefficients for elimination

Multiply the first equation by 3:

3(2x + 3y) = 3 × 23 

⇒ 6x + 9y = 69

Multiply the second equation by 2:

2(3x + 2y) = 2 × 22

⇒ 6x + 4y = 44

Step 3: Subtract the second from the first to eliminate (x) 

(6x + 9y) – (6x + 4y) = 69 – 44 

5y = 25 

y = 5

Step 4: Substitute (y = 5) into one of the original simplified equations

Using (2x + 3y = 23):

2x + 3(5) = 23 

2x + 15 = 23 

2x = 8 

x = 4