Solve the system.

  • Thread starter Kandy
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  • #1
Kandy
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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:
 

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  • #2
BobG
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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).
 
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  • #3
EnumaElish
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BobG said:
Get everything onto the same side of the equation. You have a quadratic equation.
Then, you can just use the quadratic formula to solve for the roots.
 
  • #4
robphy
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Kandy said:
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:

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.
 

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