Solve the system of equations algebraically. Show all work.

Question

y=-x^2+8x+11
y=5x-7

Answer 1

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).