How do you solve the following system?: $-2x+3y=5, -x+y=-3$

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Answer 1 · 2017-06-28T00:49:48

$x=14, y-11$

$color(white)(+)-2x+3y=5$
$color(white)(+)$
$color(white)(+)-x+y=-3$

Let's use substitution! We need to solve for $y$ in the second equation:
$-x+y=-3$

$y=-3+x$

Let's substitute $(-3+x)$ for $y$ in the first equation

$-2x+3y=5$

$-2x+3(-3+x)=5$

$-2x-9+3x=5$

$x=14$

Now we have $x$ , let's solve for $y$ :

$-2(14)+3y=5$

$-28+3y=5$

$3y=33$

$y=11$

Now we have our solutions, but to double-check, let's solve the second equation, using $14$ and $11$ for $x$ and $y$ :

$-x+y=-3$

$-(14)+11$ should give us $-3$ , if we did everything correctly

$-3=-3$ , so we were right!

How do you solve the following system?: -2x+3y=5, -x+y=-3 -2x+3y=5, -x+y=-3