substitution method for 5x-2y=8 and 2x-y=3

Question

need to solve by substitution method the following linear equations:

5x-2y=8 and 2x-y=3.

Answer 1

Substitution method

Given equations are 5x-2y = 8 ---> (1)

2x-y = 3

Subtract 2x from each side.

2x-2x-y = 3-2x

-y = -2x+3

Multiple to each side by negitive one.

y = 2x-3 ---> (2)

From (2) substitute the y value in (1).

5x-2(2x-3) = 8

5x-4x+6 = 8

x+6 = 8

Subtract 6 from each side.

x-6+6 = 8-6

x = 2

Substitute the x value in (1).

5(2)-2y = 8

10-2y = 8

Subtract 10 from each side.

10-10-2y = 8-10

-2y = -2

Divide to each side by negitive 2.

-2y/-2 = -2/-2

y = 1

Solution x = 2, y = 1.