Online notes for Math 15, Math for Liberal Arts taught in the Fall 2016 semester at Laney College by Prof. Hubbard.
6x + 5y = 182x - y = -4First determinant (denominator)| 6 5|| 2 -1| = -6 -10 = -16Swap out x column| 18 5|| -4 -1| = -18 +20 = 2Swap out y column| 6 18|| 2 -4| = -24 - 36 = -60So x = 2/-16 = -1/8and y = -60/-16 = 15/4 = 3 3/4=========3x + 7y = 122x + 5y = -18First determinant (denominator)| 3 7|| 2 5| = 15 - 14 = 1Swap out x column| 12 7|| -18 5| = 60 + 126 = 186Swap out y column| 3 12|| 2 -18| = -54 - 24 = -78So x = 186/1 = 186and y = -78/1 = -78
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6x + 5y = 18
2x - y = -4
First determinant (denominator)
| 6 5|
| 2 -1| = -6 -10 = -16
Swap out x column
| 18 5|
| -4 -1| = -18 +20 = 2
Swap out y column
| 6 18|
| 2 -4| = -24 - 36 = -60
So x = 2/-16 = -1/8
and y = -60/-16 = 15/4 = 3 3/4
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3x + 7y = 12
2x + 5y = -18
First determinant (denominator)
| 3 7|
| 2 5| = 15 - 14 = 1
Swap out x column
| 12 7|
| -18 5| = 60 + 126 = 186
Swap out y column
| 3 12|
| 2 -18| = -54 - 24 = -78
So x = 186/1 = 186
and y = -78/1 = -78
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