Answer:
(x, y) = (-2, 2)
Explanation:
You want to solve by elimination the system 4x +5y =2; -2x +2y = 8.
Observation
The x-coefficients are related by the integer factor -2. The y-coefficients are not related by an integer factor. This suggests it will be easier to eliminate the x-terms.
Since the x-terms have opposite signs, we can multiply the second equation by 2 and add it to the first to eliminate the x-terms.
Solution
Adding double the second equation to the first, we have ...
(4x +5y) +2(-2x +2y) = (2) +2(8)
9y = 18 . . . . . . . . . . simplify
y = 2 . . . . . . . . . . . divide by 9
Using the second equation to find x, we have ...
-2x +2(2) = 8
-2x = 4 . . . . . . . subtract 4
x = -2 . . . . . . . . divide by -2
The solution is (x, y) = (-2, 2).
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Additional comment
As a check on our solution, we have attached a graphical solution that gives the same result.