Solve the system of equations by substitution and enter your solution

y= x2 - 2x - 6
y= 4x + 10

The solutions are (-2, -8) and (8, 42).

Step-by-step explanation:

The given equations

y= x^2 - 2x - 6

y= 4x + 10

both give y as a function of x.  Thus, we can set them equal, which temporarily eliminates y as a variable.

Then:   x^2 - 2x - 6  = 4x + 10

Group like terms on the left:  x^2 - 6x - 16 = 0

Solve by factoring:  x^2 - 6x - 16 = 0  =  (x - 8)(x + 2) = 0.  Then x = {-2, 8}.

Using y = 4x + 10, we find the corresponding y values one by one:

y = 4(-2) + 10 = -8    and    y = 4(8) + 10 = 42.

The solutions are (-2, -8) and (8, 42).

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step-by-step explanation: