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Equation 1: 3y = 2x + 12

Slope: 2/3

X-Intercept: -6

Y-Intercept: 4

Equation 2: 2y - 4x = 12

Slope: 2

X-Intercept: -3

Y-Intercept: 6

Equation 3: 8y - 8 = 4x

Slope: 1/2

X-Intercept: -2

Y-Intercept: 1

Equation 4: 9y + 6x = -72

Slope: -2/3

X-Intercept: -12

Y-Intercept: -8

Equation 5: 4y = -8x + 32

Slope: -2

X-Intercept: 4

Y-Intercept: 8

Here is a graph showing all of the information and the simplified work:

Red line = equation 1

Blue line = equation 2

Green line = equation 3

Purple line = equation 4

Orange line = equation 5

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1