Two algebraic problems I can't solve

[stonecoldgen]

Homework Statement

1) [(1/y²)-x²]/[(1/x²)-y²]=?

2) what is the sum of the solutions, x+y, in the following system of equations?
x/y=1/2
(x+2)/(y-9)=-4/5

The Attempt at a Solution

1) I started by separating the numerator of the initial big fractionk trying to simplify but failing. However, i did get to the point where I had to separated fractions with the same denominator, but it was a fail because I was just doing a round trip, lol.

2) I defined x in terms of y and plugged it in into the (x+2)/(y-9)=-4/5 equation, being as careful as I could with having all addingg/subtracting terms with the same denominator, careful about signs etc. But I'm just doing something wrong.



BTW, I'm already a college freshman, I already passed algebra back in 9th and 10th, but I am just loosing the rhythm for this stuff and I don't want that, so any help is appreciated, thanks (just tell me which is the best path to start with if you can, thanks).

 

[micromass]

It would be nice of you to actually type out what you did!

 

[SammyS]

Homework Statement

1) [(1/y²)-x²]/[(1/x²)-y²]=?

2) what is the sum of the solutions, x+y, in the following system of equations?
x/y=1/2
(x+2)/(y-9)=-4/5

The Attempt at a Solution

1) I started by separating the numerator of the initial big fractionk trying to simplify but failing. However, i did get to the point where I had to separated fractions with the same denominator, but it was a fail because I was just doing a round trip, lol.

2) I defined x in terms of y and plugged it in into the (x+2)/(y-9)=-4/5 equation, being as careful as I could with having all adding/subtracting terms with the same denominator, careful about signs etc. But I'm just doing something wrong.

BTW, I'm already a college freshman, I already passed algebra back in 9th and 10th, but I am just loosing the rhythm for this stuff and I don't want that, so any help is appreciated, thanks (just tell me which is the best path to start with if you can, thanks).

For #1, multiply the numerator & denominator by x²y².

 

[Mentallic]

2) what is the sum of the solutions, x+y, in the following system of equations?
x/y=1/2
(x+2)/(y-9)=-4/5

2) I defined x in terms of y and plugged it in into the (x+2)/(y-9)=-4/5 equation, being as careful as I could with having all addingg/subtracting terms with the same denominator, careful about signs etc. But I'm just doing something wrong.



BTW, I'm already a college freshman, ...

If you're in college, have you learned Linear Algebra? You know, using matrices to solve linear equations? They're not necessary here, but it would be good practice to use them to solve #2 if you should already know them.

To start off, simplify both given equations into a linear combination of x and y, for example, $$\frac{x}{y}=\frac{1}{2}$$
$$2x=y$$
$$2x-y=0$$

Do the same for the second equation.

Now, we have a 3rd equation to solve, x+y=? but rather than a question mark, we'll introduce another variable, namely z for consistency.
You'll now have 3 linear equations with 3 unknowns. So either by using matrices or the conventional plugging and solving, try find the value of z.

 

[stonecoldgen]

If you're in college, have you learned Linear Algebra? You know, using matrices to solve linear equations? They're not necessary here, but it would be good practice to use them to solve #2 if you should already know them.

To start off, simplify both given equations into a linear combination of x and y, for example, $$\frac{x}{y}=\frac{1}{2}$$
$$2x=y$$
$$2x-y=0$$

Do the same for the second equation.

Now, we have a 3rd equation to solve, x+y=? but rather than a question mark, we'll introduce another variable, namely z for consistency.
You'll now have 3 linear equations with 3 unknowns. So either by using matrices or the conventional plugging and solving, try find the value of z.

hey this is pretty interesting! I am starting college today actually! I will see linear algebra next semester, but thanks a lot