# Thread: Simple simultaneous equations problem

1. ## Simple simultaneous equations problem

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.

2. 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.

3. Originally Posted by Ruscour
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.
We have: $y = x^2$ and $y = 5x-6$.

Let $x^2 = 5x-6$

Then $x^2-5x+6 = 0$

$\implies (x-3)(x-2) = 0$

$\implies x-3 = 0$ or $x-2 = 0$

$\therefore x = 3$ or $x = 2.$

4. Why did I not think of a quadratic? Who knows.

Thanks for your replies. It's interesting, as x = 3 and x = 2, the two graphs intercept each other at 2 different points, (3, 9) and (2, 4). Guess I just had a blonde moment.