9514 1404 393
Answer:
(x, y) = (43/53, 18/53)
Explanation:
If we want to eliminate the x-terms, we multiply the first equation by 7 (opposite of the x-coefficient in the second equation), and we multiply the second equation by 5 (x-coefficient in the first equation). Then we add the result.
7(5x -9y) +5(-7x +2y) = 7(1) +5(-5)
35x -63y -35x +10y = 7 -25
-53y = -18 . . . . simplify. Note the x-terms are gone.
y = 18/53 . . . . . divide by -53
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Putting this value of y in the first equation, we get ...
5x -9(18/53) = 1
5x = 1 + 162/53 = 215/53 . . . . . add 9y to both sides, simplify
x = 43/53 . . . . . . . . . . divide by 5
The solution is (x, y) = (43/53, 18/53).