system of linear functions and equations question I can't work out

[muzza]

From the Teaching Company's algebra 1 worksheet 25

Question: Solve the following system using the method of your choice:

2/x-3/y=4
1/x+4/y=-10

My problem is, I don't know how to get the equations into the y=ax+b form.
Specifically, getting y by itself and balancing the equations.

For example, I subtract 2/x to get: -3/y=-2/x+4, but don't know how to get rid of the -3 numerator and -2 numerator.

The answer is supposed to be x=-11/14, and y=-11/24

Any help much appreciated

 

[pka]

Question: Solve the following system using the method of your choice:
2/x-3/y=4
1/x+4/y=-10

\(\displaystyle 2/x-3/y=4.......[1]\\1/x+4/y=-10...[2]\)

Multiply [2] by \(\displaystyle (-2)~~\dfrac{-2}{x}+\dfrac{-8}{y}=20....[2']\) and add [2'] to [1].

 

[Deleted member 4993]

Or

substitute:

u = 1/x and v = 1/y

Then you have:

2u - 3v = 4
1u + 4v = -10

solve the above two equations by your favorite method for 'u' ( = - 14/11) & 'v' (=-24/11).

Then calculate 'x' and 'y'....

 

[muzza]

Thanks for your help.

With your help I managed to use substitution, elimination and graphing to get the same answers
x=-14/11; y=-24/11

Answer in the worksheet key is x=-11/14; y=-11/24. So, I'm guessing this is a typo.

Thanks again.