How do you solve $x+4y=-1, -3x-14=y$ by substitution?

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Answer 1 · 2016-12-07T02:15:46

$x=-5$ and $y=1$

$x+4y=-1$
$-3x-14=y$

From the second equation, we know the value of $y$ as $color(red)((-3x-14))$ . So in the first equation, substitute $y$ with $color(red)((-3x-14))$ .

$x+4y=-1$

$x+ 4color(red)((-3x-14))=-1$

Open the brackets and simplify. The product of positive and negative is a negative.

$x-12x-56=-1$

$-11x-56=-1$

Add $56$ to both sides.

$-11x=55$

Divide both sides by $11$ .

$-x=5$ or $x=-5$

In the first equation, substitute $x$ with $color(blue)(-5)$ .

$x+4y=-1$

$color(blue)(-5)+4y=-1$

Add $5$ to both sides.

$4y=4$

Divide both sides by $4$ .

$y=1$