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13a+5b=-11
13a+11b=7
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put the system of linear equations into standard form
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13x + 5y = -11
13x + 11y = 7
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solution by matrix method:
x = a = -2
y = b = 3
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system matrix
13 5
13 11
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inverse of system matrix
0.14102564 -0.064102564
-0.16666667 0.16666667
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determinant of system matrix = 78
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now solution by elimination method:
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(13a + 5b = -11)-1
13a + 11b = 7
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-13a - 5b = 11
13a + 11b = 7
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add the system:
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6b = 18
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b = 3
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13a + 5b = -11
13a + 5(3) = -11
13a = -11 - 15
13a = -26
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a = -2
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solution by elimination method:
x = a = -2
y = b = 3
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NOTE:
solution by matrix method agrees with solution by elimination method.
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