Answer:
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.
