Answer:
(-13.28, -8.14)
(1.28, -0.86)
Explanation:
We should be able to solve this in one of two approaches: graphically and algebraically. I did both.
Graphing
The DESMOS graph is attached.
There are two solutions:
(-13.28, -8.14)
(1.28, -0.86)
Mathematical
x-2y=3
x²-xy-y²=2
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x-2y=3
x = 2y + 3
----
x²-xy-y²=2
(2y+3)²-(2y+3)y-y²=2 [substitute 2y+3) for x]
(2y+3)²-(2y+3)y-y²=2
4y² +12y + 9 -2y² - 3y -y² = 2
y² + 9y + 7 = 0
y = - 0.859945
y = - 8.14005
====
x-2y=3
x = 2y + 3 [Find x for the two values of y]
(1.28, -0.8599)
(-13.28, -8.14)