Which of the following is a solution for this nonlinear system of equations

Question

X²-2x-35=y

x=y-5

Answer 1

x² - 2x - 35 = y   [1]
x = y - 5   [2]

 

Solve for y in [2]: y = x + 5

 

Substitute in [1]: x² - 2x - 35 = x + 5

 

Solve for x by factoring: x² - 3x - 40 = 0

 

(x + 5)(x - 8) = 0

 

x = -5 or 8.

 

Solve for y using [2]: If x = -5, then y = 0.

 

If x = 8, y = 13.

 

 

The solution set is {(-5, 0), (8, 13)}.