Question

What is the solution of the linear system?

-7x - 2y= -13
x = 2y + 11
O A) Infinitely many solutions
OB) (-3,2)
OC) No solution
OD) (3,-4)

Answer 1

`(3,-4)`

Explanation:

Given

`-7x - 2y = -13`

`x = 2y + 11`

Required

Find the solution

Substitute
`2y + 11` for x in the first equation

`-7(2y + 11) - 2y = -13`

Open bracket

`-14y -77 - 2y = -13`

Collect Like Terms

`-14y - 2y = -13+77`

`-16y = 64`

Solve for y

`y = (64)/(-16)`

`y = -4`

Substitute -4 for y in
`x = 2y + 11`

`x = 2(-4) + 11`

`x = -8 +11`

`x = 3`

Hence, the solution is
`(3,-4)`