Question

Solve using the method of elimination and determine if the system has 1 solution, no solutions, or infinite solutions

-7x+2y=-19
6x+8y=26

Show All work

Answer 1

-42x + 12y = -114
42x + 56y = 182
68y = 68

y = 1

6x + 8(1) =26
6x = 18

x = 3

-7(3) + 2(1) = -19
-21 + 2 = -19


One solution

Answer 2

(3,1) --> One solution

Explanation:

Start by multiplying the first equation by 4:

-7x(4)+2y(4)=-19(4)

-28x+8y=-76

In this scenario, we can eliminate 8y by subtracting the two equations:

-34x=-102

Divide both sides by -34

x=3

Plug 3 back in for x to solve for y

-7(3)+2y=-19

-21+2y=-19

Add 21 to both sides

2y=2

Divide both sides by 2

y=1

(x,y)=(3,1)