Question

6x+y=-5
y=1/2x+8
solve the system of equations using the substitution method

Answer 1

x = -2

y = 7

Explanation:

6x + y = -5 (1)

y = 1/2x + 8 (2)

by substituting the value of y from equation (2) into equation (1)

6x + 1/2x + 8 = -5

6x + 1/2x = -5 - 8

12x + x / 2 = -13

13x/2 = -13

13x = -26

x = -26/13

x = -2

by substituting the value of x in equation (2)

y = 1/2(-2) + 8

y = -1 + 8

y = 7

Answer 2

(- 2, 7 )

Explanation:

6x + y = - 5 → (1)

y =
`(1)/(2)` x + 8 → (2)

substitute y =
`(1)/(2)` x + 8 into (1)

6x +
`(1)/(2)` x + 8 = - 5 ( multiply through by 2 to clear the fraction )

12x + x + 16 = - 10 , that is

13x + 16 = - 10 ( subtract 16 from both sides )

13x + 16 - 16 = - 10 - 16 ( simplify )

13x = - 26 ( divide both sides by 13 )

`(13)/(13)` x =
`(-26)/(13)` , that is

x = - 2

substitute x = - 2 into one of the original 2 equations and solve for y

substituting into (2)

y =
`(1)/(2)` (- 2) + 8 = - 1 + 8 = 7

solution is (- 2, 7 )