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

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

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Answer 1 · 2018-03-18T01:08:43

$x = - \frac{5}{4}$ $x = -5/4$ , $y = - \frac{15}{4}$ $" "y = -15/4$

Explanation:

Eq1: $- 2 x + 2 y = - 5$ $-2x + 2y = -5$
Eq2: $x + y = - 5$ $x+y=-5$

We need to find one of the variables. Since Eq2 already has variables with coefficients of $1$ $1$ , let's start there. Let's solve for $x$ $x$ in Eq2:

Eq3: $x = - y - 5$ $x = -y-5$

Now we can use Eq3 by substituting it into Eq1. We cannot substitute into Eq2, as we have already used this equation to derive a result!

Eq3 -> Eq1:
$- 2 (- y - 5) + 2 y = - 5$ $-2(-y-5)+2y=-5$
$\Rightarrow 2 y + 10 + 2 y = - 5$ $=>2y+10+2y=-5$
$\Rightarrow 4 y + 10 = - 5$ $=>4y + 10 = -5$
$\Rightarrow 4 y = - 15$ $=>4y = -15$
$\Rightarrow y = - \frac{15}{4}$ $=> color(blue)(y = -15/4)$

We now have a value for $y$ $y$ . We have both Eq1 and Eq2 that must hold. We can use whichever one, as both will give the same results. Let's just substitute into Eq2 for convenience:

$x + (- \frac{15}{4}) = - 5$ $x+(color(blue)(-15/4))=-5$
$\Rightarrow x = - \frac{5}{4}$ $=> color(orange)(x = -5/4)$

Now we have values for both $x$ $x$ and $y$ $y$ :
$x = - \frac{5}{4}$ $x = -5/4$ , $y = - \frac{15}{4}$ $" " y = -15/4$

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

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