substitution...
x - 2y = -4.....x = 2y - 4
so we sub in 2y - 4 for x into the other equation
2x - 3y = 13
2(2y - 4) - 3y = 13
4y - 8 - 3y = 13
4y - 3y = 13 + 8
y = 21
x - 2y = -4
x - 2(21) = -4
x - 42 = -4
x = 42 - 4
x = 38
solution is (38,21)
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elimination...
2x - 3y = 13
x - 2y = -4.....multiply by -2
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2x - 3y = 13
-2x + 4y = 8 (result of multiplying by -2)
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y = 21
2x - 3y = 13
2x - 3(21) = 13
2x - 63 = 13
2x = 13 + 63
2x = 76
x = 76/2
x = 38
solution is (38,21)