4x - 9y = 6.5
-2x + 7y = -4.5
multiply the second equation by 2, then add:
4x - 9y = 6.5
-4x + 14y = -9.0
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5y = -2.5
y = -2.5/5 = -1/2
using first equation:
4x - 9(-1/2) = 6.5
4x + 4.5 = 6.5
4x = 2
x = 2/4 = 1/2
check using second equation:
-2(1/2) + 7(-1/2) = -4.5
-1 - 3.5 = -4.5
-4.5 = -4.5
x = 1/2, y = -1/2