Question

Solve the following simultaneous equations by the substitution method.

x + 2y = 5, 3x – y = 8

Answer 1

Given simultaneous equations:

x + 2y = 5, 3x – y = 8

Step 1: Express one variable in terms of the other from one equation

From the first equation:

x + 2y = 5

⇒ x = 5 – 2y

Step 2: Substitute this expression for (x) into the second equation

Substitute (x = 5 – 2y) into the second equation (3x – y = 8):

3(5 – 2y) – y = 8

Simplify:

15 – 6y – y = 8

15 – 7y = 8

–7y = 8 – 15

–7y = –7

`y = (-7)/(-7)`

y = 1

Step 3: Substitute (y = 1) back into (x = 5 – 2y)

x = 5 – 2(1)

x = 5 – 2

x = 3