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First, change 2x+6y=32 to x+3y=16. Then solve for x, which is x=-3y+16. Then substitute -3y+16 as x into 5x-2y=12 and solve for y.

5(-3y+16)-2y=12

-15y+80-2y=12

-17y+80=12

-17y=-68

y=4

Then substitute 4 as y in either equation to solve for x.

5x-2(4)=12

5x-8=12

5x=20

x=4

The answer is x=4 and y=4, or (4,4)

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