# Thread: Systems of Liner Equations

1. ## Systems of Liner Equations

I know how to solve systems of linear equations using 2 equations. I can even solve a system of linear equations with 3 quations using Gaussian Elimination. But, for some reason, I cannot solve this one. I've plugged it into wolframalpha's engine to see what the correct answers are, but it does not show the steps. Any help would be greatly appreciated.

$\displaystyle 2/x + 3/y = -2$
$\displaystyle 4/x - 5/y = 1$

2. Originally Posted by franzpulk
I know how to solve systems of linear equations using 2 equations. I can even solve a system of linear equations with 3 quations using Gaussian Elimination. But, for some reason, I cannot solve this one. I've plugged it into wolframalpha's engine to see what the correct answers are, but it does not show the steps. Any help would be greatly appreciated.

$\displaystyle 2/x + 3/y = -2$
$\displaystyle 4/x - 5/y = 1$
multiply every term in the first equation by -2 and combine to eliminate the x terms ...

-4/x - 6/y = 4

4/x - 5/y = 1
---------------

-11/y = 5

y = -11/5

sub the value for y into either original equation and solve for x ...

2/x - 15/11 = -2

2/x = -7/11

x = -22/7

3. I got it now. I was multiplying both through by xy to begin with instead of eliminating one and then multiplying through by xy.

Thanks.