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X-2y=2

2x+4y=36

x = 10, y = 4

Step-by-step explanation:

Solve the following system:

{x - 2 y = 2 | (equation 1)

2 x + 4 y = 36 | (equation 2)

Swap equation 1 with equation 2:

{2 x + 4 y = 36 | (equation 1)

x - 2 y = 2 | (equation 2)

Subtract 1/2 * (equation 1) from equation 2:

{2 x + 4 y = 36 | (equation 1)

0 x - 4 y = - 16 | (equation 2)

Divide equation 1 by 2:

{x + 2 y = 18 | (equation 1)

0 x - 4 y = - 16 | (equation 2)

Divide equation 2 by - 4:

{x + 2 y = 18 | (equation 1)

0 x+y = 4 | (equation 2)

Subtract 2 * (equation 2) from equation 1:

{x+0 y = 10 | (equation 1)

0 x+y = 4 | (equation 2)

Collect results:

Answer: {x = 10, y = 4

Rearrange first equation

2y = x-2

X = 2y + 2

Plug in values

2 (2y+2) + 4y = 36

4y + 4 + 4y=36

8y+4 = 36

8y=32

Y=4

Solved for y, now plug in to find x.

2y=x-2

2 (4) = x - 2

8 = x-2

X = 10