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

(-13.28, -8.14)

(1.28, -0.86)

Step-by-step 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)