Thread: Solving by substitution, elimaination and graphing method

1. Solving by substitution, elimaination and graphing method

How do I solve the equations x squared - y squared=1
2x squared - y squared= x+3 using substitution, elimination and graphing method?

2. Re: Solving by substitution, elimaination and graphing method

What, exactly, is your difficulty? Do you not know what any of those words mean?

To solve a pair of equation "by substitution" means to solve one equation for something and substitute that into the othe equation. Solve the equation $x^2- y^2= 1$ for $y^2$ as a function of x (or $x^2$) and then substitute that into $2x^2- y^2= x+ 3$.

To solve a pair of equation "by elimination" means to algebraically combine the two equation to eliminate one of the unknowns. Here, I suggest that you subtract $x^2- y^2= 1$ from $2x^2- y^2= x+ 3$ eliminating y.

Finally, to solve a pair of equations "by graphing" means to do exactly that- graph both equations and see where the graphs intersect.

With each of those methods, I get 3 distinct solutions.

3. Re: Solving by substitution, elimaination and graphing method

I realize the steps however when I do the arithmetic is doesnt seem to come out right. I think Im doing something wrong but I dont know what. I need to see it worked out to figure out where I went wrong.

4. Re: Solving by substitution, elimaination and graphing method

A better approach would be for you to post what you have, then someone here can point out where you are going wrong. This will do two things...demonstrate that you are making a genuine effort and help you find exactly where the error in your approach is, and then you can avoid this error in the future.

5. Re: Solving by substitution, elimaination and graphing method

when I solved for x in the equation x^2 - y^2=1 I got x=y+1, is that correct? If so when I plugged it into the equation 2x^2-y^2=x+3 and got the variables set to zero I got y^2+3y-2=0 (this is in regards to the substitution method.)

6. Re: Solving by substitution, elimaination and graphing method

No, I suggest you read carefully the suggestions provided by HallsofIvy, and follow the steps he has provided.

For example, he suggests solving $x^2-y^2=1$ for $y^2$...what do you get?

7. Re: Solving by substitution, elimaination and graphing method

This is the steps I took in that regards are subtracting x^2 and got the equation y^2=1-x^2 I then took the square root of each side and got y=1-x

8. Re: Solving by substitution, elimaination and graphing method

You don't need to take the square root of each side (and you did so incorrectly), because the second equation contains $y^2$. Try again to solve for $y^2$ as you did not get it quite right. Add $y^2-1$ to both sides.

9. Re: Solving by substitution, elimaination and graphing method

Originally Posted by derek1008
when I solved for x in the equation x^2 - y^2=1 I got x=y+1, is that correct?
No, that is NOT correct. You can get x^2= y^2+ 1 but the square root of y^2+ 1 is NOT y+ 1 For example, if y= 2 y^2+ 1= 5. The square root of 5 is NOT equal to 2+ 1= 3!

When I plugged it into the equation 2x^2-y^2=x+3 and got the variables set to zero I got y^2+3y-2=0 (this is in regards to the substitution method.)