Question

Solve the system of equations 2x+3y=40 and -2x+2y=20.

Answer 1

2x + 3y = 40 (1)
-2x + 2y = 20 (2)

Multiply throughout (2) by negative one to get the x term positive
-(-2x) + -1(2y) = -1(20)
2x - 2y = -20 (3)

Make 2x the subject of (3)
2x - 2y = -20
2x = 2y - 20

Substitute expression for 2x into (1)
(2y - 20) + 3y = 40

Expand and then solve for y
2y + 3y = 60
5y = 60
y = 12

Substitute value of y into equation (3) and solve for x
2x - 2y = -20
2x - 2(12) = -20
2x = -20 + 24

x =
`(4)/(2)`
= 2

∴ y = 12 ; x = 2