The line y=2-3x intersects the curve x^2-y=2

Let's see if we can solve this......

In the second equation, we can add y to both sides and subtract 2 from both sides.

So we have

y = x^2 - 2     and

y = -3x + 2     So setting the "y's" equal, we have

x^2 - 2 = -3x + 2     Subtracting everything on the right on both sides, we have

x^2 + 3x - 4 = 0       And factoring, we have

(x + 4) (x - 1) = 0     And setting both factors to 0, we have

x = -4 and x = 1        And using y = -3x + 2 and substituting both values of x

We find that y = 14 when x = -4 and y =  -1 when x = 1

So our solutions are  (-4, 14)  and ( 1, -1)

di you know how to use systems (of equations)

(1,-1) and (-4, 14)