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

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Answer 1 · 2016-05-05T19:35:49

$x=-7$
$y=1$

Given:
$" "4x+5y=-23$ ...........................(1)
$" "x=-2-5y$ ..................................(2)

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

$" "4(-2-5y)+5y=-23" "...................(1_a)$

Multiply out the bracket

$" "-8-20y+5y=-23$

$color(brown)(" "-8-15y=-23)$

Add $color(blue)(15y)$ to both sides

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

But $color(brown)(-15y)color(blue)(+15y)color(green)(=0)$

$-8color(green)(+0)=-23+15y$

Add 23 to both sides

$-8+23=15y$

$15=15y$
Divide both sides by 15
$y=1$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substitute $y=1$ into equation (2)

$x=-2-5(1) = -7$

How do you solve 4x+5y=-234x+5y=-23 and x= -2-5yx= -2-5y using substitution?