# How do you solve 4x+5y=-23 and x= -2-5y using substitution?

May 5, 2016

$x = - 7$
$y = 1$

#### Explanation:

Given:
$\text{ } 4 x + 5 y = - 23$ ...........................(1)
$\text{ } x = - 2 - 5 y$..................................(2)

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Substitute for $x$ in equation (1) using equation (2) giving:

$\text{ "4(-2-5y)+5y=-23" } \ldots \ldots \ldots \ldots \ldots \ldots . \left({1}_{a}\right)$

Multiply out the bracket

$\text{ } - 8 - 20 y + 5 y = - 23$

$\textcolor{b r o w n}{\text{ } - 8 - 15 y = - 23}$

Add $\textcolor{b l u e}{15 y}$ to both sides

color(brown)(" -8-15ycolor(blue)(+15y)=-23color(blue)(+15y))

But $\textcolor{b r o w n}{- 15 y} \textcolor{b l u e}{+ 15 y} \textcolor{g r e e n}{= 0}$

$- 8 \textcolor{g r e e n}{+ 0} = - 23 + 15 y$

$- 8 + 23 = 15 y$
$15 = 15 y$
$y = 1$
Substitute $y = 1$ into equation (2)
$x = - 2 - 5 \left(1\right) = - 7$