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Use the elimination method to solve the system of equations. 6x-2y=52 5x+3y=34

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Solve the following system:

{-2 y + 6 x = 52 | (equation 1)

3 y + 5 x = 34 | (equation 2)

Subtract 5/6 x(equation 1) from equation 2:

{6 x - 2 y = 52 | (equation 1)

0 x + (14 y)/3 = -28/3 | (equation 2)

Divide equation 1 by 2:

{3 x - y = 26 | (equation 1)

0 x + (14 y)/3 = -28/3 | (equation 2)

Multiply equation 2 by 3/14:

{3 x - y = 26 | (equation 1)

0 x + y = -2 | (equation 2)

Add equation 2 to equation 1:

{3 x + 0 y = 24 | (equation 1)

0 x + y = -2 | (equation 2)

Divide equation 1 by 3:

{x + 0 y = 8 | (equation 1)

0 x + y = -2 | (equation 2)

Answer: x = 8 y = -2

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