Use the substitution method to find the solution(s) to the system of equations. Show all work for full credit.
y = x2 – 1
y = –x – 1

Question

Use the substitution method to find the solution(s) to the system of equations. Show all work for full credit.
y = x2 – 1
y = –x – 1

pfenn1 · Answer

Do you know the substitution method?

anonymous · Answer

no not really, i know you have to put one equation in the other...

pfenn1 · Answer

Correct. The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable. http://www.purplemath.com/modules/systlin4.htm

anonymous · Answer

could you walk me through this problem step by step so i can be able to do the rest by myself?

pfenn1 · Answer

Okay both equations are already solved for y in terms of x.  We know that $$y=x^2-1$$$$y=x-1$$  Okay.  So let's substitute the second equation for the y in the first equation.  What do you  get?

anonymous · Answer

the ones cancel and were left with x=x^2?

pfenn1 · Answer

Yep.  And what does that mean?

anonymous · Answer

so do we subtract x from x^2? or square root it?

pfenn1 · Answer

Do you know of any numbers that x=x^2 is the solution?

pfenn1 · Answer

I mean, the square of an number equals the value of the number?

anonymous · Answer

would it be 1?

pfenn1 · Answer

It is the only solution I can think of that works.

anonymous · Answer

okay then we put 1 into the x for the second equation right?

pfenn1 · Answer

Yes.  I forgot that there were two equations and two variables.  LOL

anonymous · Answer

so the final answer is y=-2, x=1?

pfenn1 · Answer

You know, I screwed up.  That is one answer.  But there is a second answer. If we plug 1 into the first equation we get y=0.

anonymous · Answer

its okay i get the jist of it!

pfenn1 · Answer

ok.