# How do you solve 4x+5y=21 and -3x+ y =27 using substitution?

Mar 29, 2016

$\textcolor{b r o w n}{\text{Only demonstrating a different approach}}$
This uses substitution to find $y$ if you plug the value of $x$ into one of the equations. However I should think they were looking for the method the others used.

#### Explanation:

Given

$\textcolor{w h i t e}{\ldots . .} 4 x + 5 y = 21$...............................(1)
$\textcolor{w h i t e}{.} - 3 x + y = 27$.................................(2)

Multiply equation (2) by 5 giving:

$\textcolor{w h i t e}{\ldots \ldots .} 4 x + 5 y = 21$...............................(1)
$\underline{\textcolor{w h i t e}{.} - 15 x + 5 y = 135} \text{ } \ldots \ldots \ldots \ldots \ldots \left({2}_{a}\right)$
$\textcolor{w h i t e}{\ldots \ldots} 19 x + \textcolor{w h i t e}{.} 0 = - 114 \text{ } \to$ Subtract equation $\left({2}_{a}\right)$ from (1)

$\implies x = - \frac{114}{19} = - 6$

Then solve as the others did