Solve the system of equations algebraically. Show all work.
y=-x^2+8x+11
y=5x-7
Since both expressions are equal to y, we can set them equal to each other:
-x^2+8x+11=5x-7
Now we can simplify and solve for x:
-x^2+3x+18=0
Multiplying both sides by -1:
x^2-3x-18=0
This can be factored into:
(x-6)(x+3)=0
Therefore, x=6 or x=-3.
Now we can substitute these values back into one of the original equations to solve for y. Using y=5x-7:
When x=6,
y=5(6)-7=23
When x=-3,
y=5(-3)-7=-22
Therefore, the solution is (6,23) and (-3,-22).