Question

answer and shown work for 5x + y = 10 -x - y = -2

Answer 1

Solve first equation for y: 
5x+y=10
y=10-5x. Plug this equation into second equation

-x-(10-5x)=-2
-x-10+5x=-2
4x=8
x=2 (plug x into first equation)

5(2)+y=10
y=0

Answer 2

5x+y = 10
-x-y = -2
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4x = 8
x = 2
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-x-y = -2
-2-y = -2
-y = 0
y = 0
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Check:
5x+y = 10 
5(2)+0 = 10
10+0 = 10
10 = 10
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Solution : x=2, y=0