Question

Solve the following simultaneous equations by the substitution method.

x + 5y = 28, 4x + 15y = 87

Answer 1

Given simultaneous equations: x + 5y = 28, 4x + 15y = 87

Step 1: Express (x) in terms of (y) from the first equation: 

x = 28 – 5y

Step 2: Substitute (x = 28 – 5y) into the second equation: 

4(28 – 5y) + 15y = 87

Step 3: Simplify and solve for (y): 

112 – 20y + 15y = 87 

⇒ 112 – 5y = 87

–5y = 87 – 112

–5y = –25 

⇒ `y = (-25)/(-5)`

⇒ y = 5

Step 4: Substitute (y = 5) back into (x = 28 – 5y):

x = 28 – 5 × 5

x = 28 – 25 

x = 3