Question

Solve the following simultaneous equations by the substitution method.

x + y = 3, x – 7y = –5

Answer 1

Given simultaneous equations:

x + y = 3   ...(1)

x – 7y = –5   ...(2)

Step 1: Express (x) from equation (1): 

x = 3 – y

Step 2: Substitute (x = 3 - y) into equation (2): 

(3 – y) – 7y = –5 

3 – y – 7y = –5 

3 – 8y = –5

Step 3: Solve for (y): 

–8y = –5 – 3 

–8y = –8 

`y = (-8)/(-8)`

y = 1

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

x = 3 – 1

x = 2