1. 2x + y = 3
-x + 3y = -12 => multiply by 2
2x + y = 3
2(-x) + 2(3y) = 2(-12)
2x + y = 3
-2x + 6y = -24 Now add the equations
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7y = -21
y = -3 Substitute back into equation
2x + y = 3
2x + (-3) = 3
2x = 6
x = 6/2 = 3
(3, -3)
2. 6x + 5y = 19
2x + 3y = 5 => multiply by -3 so the x's will cancel
6x + 5y = 19
(-3)2x + (-3)3y = -3(5)
6x + 5y = 19
-6x - 9y = -15 now add the 2 equations
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-4y = 4
y = -1 now substitute back into the equation
2x + 3y = 5
2x + 3*-1 = 5
2x - 3 = 5
2x = 8
x = 8/2 = 4
(4,-1)
3. 2x + 5y = 16 => multiply by 2 so x's cancel
-4x + 3y = 20
(2)2x + (2)5y = (2)16
4x + 10y = 32
-4x + 3y = 20 add the equations
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13y = 52
y = 52/13 = 4 substitute into unchanged equation
-4x + 3(4) = 20
-4x + 12 = 20
-4x = 8
x = 8/-4 = -2
(-2, 4)