What are the solutions to the system of equations?

y=x^2−5x−6 y=2x−6

(−6,0) and (0,−1)

(−1,0) and (−6,0)

(7, 8) and (0,−6)

(−1,0) and (0,−6)

The answer is (7, 8) and (0,−6).

Step-by-step explanation:

The given system has two equations, one is the linear and the other is non-linear.

Let,

y = x^2 - 5x - 6    equation 1

y = 2x - 6    equation 2

Step 1: Equating both equations for the value of x

x^2 - 5x - 6 = 2x -6

x^2 -5x +5x - 6 = 2x + 5x - 6

x^2 -6 +6 = 7x -6 +6

x^2 - 7x  = 7x - 7x

x^2 -7x = 0

x ( x - 7) = 0

implies that,

x = 0  OR  x - 7 = 0 ⇒ x = 7

Now pick any of the two equations of y to find the solution. I'll choose the equation 2.

the value of y, for x = 0

y = 2(0) - 6  

y = - 6

the value of y, for x  = 7

y = 2(7) -6

y = 14 - 6

y = 8

hence, (0,-6) and (7, 8) are the solutions to the given system of equations.