Question

Solve the following system of equations by the elimination method:

4x + 3y = 13, x + y = 4

Answer 1

Given system of equations: 4x + 3y = 13, x + y = 4

Step 1: Multiply the second equation by 3 to align the coefficient of (y)

3(x + y) = 3 × 4 

⇒ 3x + 3y = 12

Step 2: Subtract the second new equation from the first

(4x + 3y) – (3x + 3y) = 13 – 12

4x – 3x + 3y – 3y = 1

x = 1

Step 3: Substitute (x = 1) into (x + y = 4) to find (y)

1 + y = 4

⇒ y = 3

x = 1, y = 3

So, the solution to the system is (1, 3).