Question

the solution sets of
x+y=5
y=x^2-10x-9

Answer 1

To find the solution set, we need to solve the system of equations:

1) x + y = 5
2) y = x^2 - 10x - 9

Substituting equation 1) into equation 2) to eliminate y, we have:

x + (5 - x) = x^2 - 10x - 9

Simplifying gives:

5 = x^2 - 10x - 9

Rearranging the equation:

x^2 - 10x - 14 = 0

Factoring the quadratic equation:

(x - 14)(x + 1) = 0

Setting each factor equal to zero:

x - 14 = 0 --> x = 14
x + 1 = 0 --> x = -1

So the possible x-values in the solution set are x = 14 and x = -1.

Substituting these values back into equation 1) to solve for y:

For x = 14: 14 + y = 5 --> y = -9
For x = -1: -1 + y = 5 --> y = 6

Therefore, the solution set for the system of equations is {(14, -9), (-1, 6)}.