# Solve the system.

1. Sep 14, 2005

### Kandy

y=x^2
y=x-1/4

I really need help with this question. i don't know how to do these types of questions with fractions. i can't think, i need to sleep :zzz:

2. Sep 15, 2005

### BobG

Edit: I jumped a step. Both equations are equal to y, so $$x^2=x-\frac{1}{4}$$

Get everything onto the same side of the equation. You have a quadratic equation.

Factoring fractions really isn't that much different than integers. You figure out the combinations that will equal 1/4 when multiplied together. For example:

$$\frac{1}{4}* 1 = \frac{1}{4}$$
$$\frac{1}{2}*\frac{1}{2} = \frac{1}{4}$$

and so on. Add the combinations together and hopefully one of them will equal your middle coefficient (1 in this case).

Last edited: Sep 15, 2005
3. Sep 15, 2005

### EnumaElish

Then, you can just use the quadratic formula to solve for the roots.

4. Sep 15, 2005

### robphy

Note that y=x-1/4 can be rewritten as 4y=4x-1. (No fractions here!)

As BobG suggests, since y=x^2 replace y in (4y=4x-1) by x^2:
4(x^2)=4x-1.

Then, as EnumaElish suggests, use the quadratic formula [after writing it in standard form].

An alternate method is to plot the two curves (one is a parabola and one is a line) then locate the intersection points.