# How do you solve 5x + 8y = 7 and x + y = 2 using substitution?

Apr 24, 2016

x=3, y= -1

#### Explanation:

given x+y=2
y= 2 - x (eq. 1)

given 5x+8y=7 (eq.2)

substitute eq. 1 in eq. 2

5x + 8(2-x) =7
5x + 16 - 8x = 7 (open the bracket)
-3x=7-16= -9
x= -9/ -3 = 3

eq 1-
y= 2-3= -1

so x=3, y= -1

Apr 24, 2016

$\left(x , y\right) = \left(3 , - 1\right)$
See below for method of solution by substitution.

#### Explanation:

If $x + y = 2$
then $y = 2 - x$
and
$\textcolor{w h i t e}{\text{XXX}} \left(2 - x\right)$ can be substituted for $y$ in $5 x + 8 y = 7$

This would give:
$\textcolor{w h i t e}{\text{XXX}} 5 x + 8 \left(2 - x\right) = 7$

$\textcolor{w h i t e}{\text{XXX}} 5 x + 16 - 8 x = 7$

$\textcolor{w h i t e}{\text{XXX}} - 3 x = - 9$

$\textcolor{w h i t e}{\text{XXX}} x = 3$

Then, returning to $y = 2 - x$
we have
$\textcolor{w h i t e}{\text{XXX}} y = 2 - 3 = - 1$