Question

Solve the following simultaneous equations by the substitution method.

2x + y = 4, 3x + 2y = 7

Answer 1

Given the simultaneous equations:

2x + y = 4 and 3x + 2y = 7

Step 1: Express (y) from the first equation

From 2x + y = 4, y = 4 – 2x

Step 2: Substitute (y) in the second equation

Substitute y = 4 – 2x into 3x + 2y = 7:

3x + 2(4 – 2x) = 7 

3x + 8 – 4x = 7

x + 8 = 7

–x = –1 

x = 1 

Step 3: Substitute (x = 1) back into (y = 4 - 2x)

y = 4 – 2 × 1

y = 4 – 2 

y = 2