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16 votes
16 votes
Solve for x and y simultaneously:
x-2y=3
x²-xy-y²=2 ​

User Mohammad Ranjbar Z
by
2.9k points

1 Answer

17 votes
17 votes

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 ​

=====

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)

Solve for x and y simultaneously: x-2y=3 x²-xy-y²=2 ​-example-1
User Helen Wood
by
3.1k points