Systems of equations using substitution 3 x+4 y=-31 x+y=6

3x+4y=-31

x+y=6

multiply second equation by - 3

-3x-3y=-18

add to first equation

3x+4y=-31

-3x-3y=-18 +

0x+y=-49

y=-49

subsitute

x+y=6

x-49=6

add 49 to both sides

x=55

the solution is (x, y) form is

(55,-49)

3x + 4y = - 31

x + y = 6

Rewrite the second one (because it's more convenient) : y = 6-x

Replace in the first equation: 3x + 4 (6-x) = - 31

Simplify: 3x + 24 - 4x = - 31

Simplify: - 1x + 24 = - 31

Subtract: - 1x = - 31 - 24

Simplify:-1x = - 55 or x=55

Plug into the first equation: 55+y=6

Subtract: y=6-55 or y = - 49

Answer: x=55, y=-49

Verify:

x+y = 6

55-49=6? True

3x + 4y = - 31

3 (55) + 4 (-49) = - 31?

165-196=-31? True