Answer:
(x, y) = (-6, -10)
Step-by-step explanation:
Pick a variable whose coefficient you want to be zero in the sum. Note the two coefficients of that variable in the two equations. Write the second coefficient in the first box, and the opposite of the first coefficient in the second box.
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If you want to eliminate x-terms, the x-coefficients are -2 and -3. Write -3 in the first box and +2 in the second box.
-3(-2x +2y = -8) ⇒ 6x -6y = 24
+2(-3x +y = 8) ⇒ -6x +2y = 16
Added together, the resulting equation is ...
0x -4y = 40
y = -10 . . . . . . . divide by -4
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If you want to eliminate y-terms, the y-coefficients are 2 and 1. Write 1 in the first box, and -2 in the second box.
1(-2x +2y = -8) ⇒ -2x +2y = -8
-2(-3x +y = 8) ⇒ 6x -2y = -16
Added together, the resulting equation is ...
4x +0y = -24
x = -6 . . . . . . . . divide by 4
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Now, you know the solution is (x, y) = (-6, -10).
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Additional comment
It does not matter which is the first equation. You can swap the two equations and still achieve the desired results. Also, if the coefficients have a common factor, you can divide that out. As you may have noticed, the arithmetic is a little easier if one of the chosen coefficients is 1 or -1.
If you're combining the equations using addition, as we have done here, then one of the coefficient multipliers must be negated, as we have described. If you're combining the equations using subtraction, then you can preserve the original signs of the coefficients (or change them both).
