Solve each system by substitution?

Question

1)y = 5x - 10
y = 3x + 8

2)3x + y = 2
4x + y = 20

Answer 1

1) The system of equations are y = 5x - 10, y = 3x + 8.

substitute y = 5x - 10 in equation y = 3x + 8
5x - 10 = 3x + 8

subtract 3x from each side
2x - 10 = 8

add 10 to each side
2x = 18

Divide each side by 2
x = 9.

substitute x = 9 in y = 3x + 8
y = 3 * 9 + 8 = 35

(x, y) = (9, 35)

2) The system of equations are 3x + y = 2, 4x + y = 20.

3x + y = 2

Rewrite the equation interms of y.

y = 2 - 3x

Substitute y = 2 - 3x in 4x + y = 20

4x + 2 - 3x = 20

x + 2 = 20

subtract 2 from each side

x = 18

substitute x = 18 in y = 2 - 3x

y = 2 - 3 * 18

y = 2 - 54 = -52

(x, y) = (18, -52)