Given:
The two equations are:
[tex]y=\dfrac{2}{3}x-5[/tex]
[tex]y=-2x+3[/tex]
To find:
Whether (-3,-3) is a solution of the given equation or not.
Solution:
Table of values for [tex]y=\dfrac{2}{3}x-5[/tex],
x y
0 -5
7.5 0
Plot the points (0,-5) and (7.5,0) on a coordinate plane and connect them by a straight line.
Table of values for [tex]y=-2x+3[/tex],
x y
0 3
1.5 0
Plot the points (0,3) and (1.5,0) on a coordinate plane and connect them by a straight line.
From the below graph, it is clear that the graphs of both lines intersect each other at (3,-3). So, the solution of given equations is (3,-3) instead of (-3,-3).
Therefore, she is incorrect because the correct solution is (3,-3).