Question

Solve the following simultaneous equations by the substitution method.

0.2x + 0.5y = 2.1, 0.3x + 0.4y = 2.8

Answer 1

Given simultaneous equations:

0.2x + 0.5y = 2.1, 0.3x + 0.4y = 2.8

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

From equation (1):

0.2x + 0.5y = 2.1

⇒ 0.2x = 2.1 – 0.5y 

`x = (2.1 - 0.5y)/(0.2)`

x = 10.5 – 2.5y

Step 2: Substitute (x) into equation (2)

Substitute (x = 10.5 – 2.5y) into equation (2):

0.3(10.5 – 2.5y) + 0.4y = 2.8 

3.15 – 0.75y + 0.4y = 2.8 

3.15 – 0.35y = 2.8 

–0.35y = 2.8 – 3.15 

–0.35y = –0.35

`y = (-0.35)/(-0.35)`

y = 1

Step 3: Find (x) using the value of (y)

Put (y = 1) into the expression for (x):

x = 10.5 – 2.5(1)

x = 10.5 – 2.5

x = 8