Just as a forewarning, I have no idea why I can't solve this and I feel unbelievably dumb.
y = x^2
y = 5x - 6
Graphically it is seen that y = 4 and x = 2, but how do I solve it algebraically? Thanks in advance.
If you want both equations to be true, you have that y = x^2, and that y = 5x - 6.
In that case, x^2 = 5x - 6. Can you see why?
Now you have a quadratic equation in x, which should be easy to solve.
Also, don't forget, there are two points of intersection. You've found one; now you should be able to find the other.
We have: $\displaystyle y = x^2$ and $\displaystyle y = 5x-6$.
Let $\displaystyle x^2 = 5x-6$
Then $\displaystyle x^2-5x+6 = 0 $
$\displaystyle \implies (x-3)(x-2) = 0$
$\displaystyle \implies x-3 = 0$ or $\displaystyle x-2 = 0$
$\displaystyle \therefore x = 3$ or $\displaystyle x = 2.$