Answer:
(8, -1)
Step-by-step explanation:
We note that the coefficients of y are opposites, so when we add these equations, the y-terms will cancel:
(3x -8y) +(-x +8y) = (32) +(-16)
2x = 16 . . . . simplify
x = 8 . . . . . . divide by 2
-8 +8y = -16 . . . substitute into the second equation
-1 +y = -2 . . . . . divide by 8
y = -1 . . . . . . . . add 1
The solution is (x, y) = (8, -1).
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Comment on systems of equations
There are formulas for the solution of a system of equations like this. However, we are taught several methods that can be used instead of the formulas. One of my favorite is graphing, now that graphing calculators and apps are available on-line and on your local smart device. Other ad hoc methods include "elimination" or "addition", and "substitution." Using these methods can often save steps over using a formula, which is partly why they're taught.
