Question

Solve for this equation algebraically for all values of x and y.
y= x^2 + 2x - 8 and y= 2x + 1

Answer 1

Since the second equation conveniently isolates y for you, we can just go ahead and plug this into your first equation.
Therefore:
2x + 1 = x^2 + 2x - 8

Moving all the values to one side gives us:
0 = x^2 - 9

Knowing that (x^2 - y^2) = (x-y)(x+y), this can be broken down into:
0 = (x-3)(x+3)

So x = 3 or -3
Now we can just plug these values of x into the second equation and get that y = 7 or -5.

Answer 2

ohhhh that makes so much sense thank you!