# How do you solve the system of equations -2x+4y=7 and ?

Nov 5, 2017

Suppose the second equation was : $4 x - y = 0$
then
$\textcolor{w h i t e}{\text{XXX}} \left(x , y\right) = \left(\frac{1}{2} , 2\right)$

#### Explanation:

The only way to clear this question (after a year with no correction) seems to be to add the missing component. The additional equation $4 x - y = 0$ was completely arbitrary.

[1]$\textcolor{w h i t e}{\text{XXX}} - 2 x + 4 y = 7$
[2]$\textcolor{w h i t e}{\text{XXX}} 4 x - y = 0$

Multiplying [1] by $2$
[3]$\textcolor{w h i t e}{\text{XXX}} - 4 x + 8 y = 14$

[4]$\textcolor{w h i t e}{\text{XXX}} 7 y = 14$
Dividing both sides of [4] by $7$
[5]$\textcolor{w h i t e}{\text{XXX}} y = 2$
Substituting $2$ for $y$ in [2]
[6]$\textcolor{w h i t e}{\text{XXX}} 4 x - 2 = 0$
[7]$\textcolor{w h i t e}{\text{XXX}} 4 x = 2$
[8]$\textcolor{w h i t e}{\text{XXX}} x = \frac{1}{2}$