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

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Answer 1 · 2017-06-28T00:49:48

$x = 14, y - 11$ $x=14, y-11$

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

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

$y = - 3 + x$ $y=-3+x$

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

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

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

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

$x = 14$ $x=14$

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

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

$- 28 + 3 y = 5$ $-28+3y=5$

$3 y = 33$ $3y=33$

$y = 11$ $y=11$

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

$- x + y = - 3$ $-x+y=-3$

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

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

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