Question

What is the solution to the system that is created by the equation y=-x+6 and the graph shown below

Answer 1

If you draw the graph of y = -x + 6  on the above graph  the solution to system will be the coordinates of the point of intersection.
the equation of the line drawn above is y = 0.5x

so you can also find the solution by solving the system
y = 0.5x
y = -x + 6

0.5x = -x + 6
1.5x = 6
x = 6/1.5 = 4

and y = 0.5*4 = 2

The answer is  (4, 2)     - the third choice.

Answer 2

If you were to plot the function y=-x+6, both functions meet at the point (4,2)