Solve the system.

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

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:

[tex]\frac{1}{4}* 1 = \frac{1}{4}[/tex]
[tex]\frac{1}{2}*\frac{1}{2} = \frac{1}{4}[/tex]

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

 

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

 

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.