To find the values of x and y that satisfy both equations, we need to solve these two equations simultaneously. This is a system of equations that can be solved using several methods. One easy method is to use the method of substitution or elimination.
First, observe the two equations:
1) 4x - 9y = 18
2) -2x + 2y = 16
We can observe that if we multiply the second equation by 2, it will result in the equation having the same coefficient for x as the first equation:
-4x + 4y = 32
Now we have:
1) 4x - 9y = 18
2) -4x + 4y = 32
We can add these two equations, which will eliminate x:
4x - 9y - 4x + 4y = 18 + 32
-5y = 50
Dividing each side by -5, we find:
y = -10
Now that we have y, we can substitute -10 for y in either of the original equations. Using the first equation:
4x - 9*(-10) = 18
4x + 90 = 18
4x = -72
x = -72 / 4
x = -18
Therefore, the solution to this system of equations is x = -18 and y = -10. That is the point where the lines represented by these two equations intersect.