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Answer:
5) (x, y) = (10, -1)
6) (x, y) = (5, 6)
Explanation:
5) y coefficients are opposites, so y can be eliminated by adding the two equations.
(x -y) +(2x +y) = (11) +(19)
3x = 30 . . . . . simplify
x = 10 . . . . . . . divide by 3
Using the second equation, we can find y:
2(10) +y = 19
y = -1 . . . . . subtract 20
The solution is (x, y) = (10, -1).
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6) The x-coefficients are the same, so we can eliminate the x-term by subtracting the second equation from the first. We choose to do it that way so the y-coefficient ends up positive.
(-6x +6y) -(-6x +3y) = (6) -(-12)
3y = 18 . . . . . . simplify
y = 6 . . . . . . . . divide by 6
Using the first equation to find x, we have ...
-6x +6(6) = 6
x -6 = -1 . . . . . . . divide by -6
x = 5 . . . . . . . . . add 6
The solution is (x, y) = (5, 6).