The first equation contains a +2y term and the second contains a -2y term. So if we add the two equations, it will eliminate the y variable so we can solve for x:
7x + 2y = 6
6x - 2y = 8
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13x + 0 =14
13x = 14
x = 14/13
To find y, plug x=14/13 into either original equation and solve for y:
7x + 2y = 6
7(14/13) + 2y = 6
(98/13) + 2y = 6
2y = 6 - (98/13)
2y = -20/13
y = -10/13
Check:
7x+2y = 6
7(14/13) + 2(-10/13) = 6
98/13 - 20/13 = 6
78/13 = 6
6 = 6
6x - 2y = 8
6(14/13) - 2(-10/13) = 8
84/13 + 20/13 = 8
104/13 = 8
8 = 8
