How do you solve the system 3x - 2y = 8 and 2x + 5y = -1?

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Answer 1 · 2017-06-25T08:27:31

$x=2, y=-1$

This is a clear simultaneous equation.

$3x-2y=8$
$2x+5y=-1$

In order to solve this, either the x's or the y's must be balanced. It does not matter which one you start with.

For this, I'll balance the y's:

$15x-10y=40$ Every value is multiplied by 5.
$4x+10y=-2$ Every value is multiplied by 2.

Both y values can now be eliminated.

$15x-10y+4x+10y=19x$
$40-2=38$

$19x=38$

Now solve for x.

$x=38/19=2$

Put the value for x back into either equation to find y.

$3x-2y=8$
$3(2)-2y=8$
$6-2y=8$
$-2y=8-6=2$

Rearrange to find y.

$-2y=2$

Divide both sides by -2.

$y=2/-2$

$y=-1$