# How do you solve 3x + y = 3, x - 4y = 1?

Mar 21, 2018

$\left(x , y\right) \to \left(1 , 0\right)$

#### Explanation:

$3 x + y = 3 \to \left(1\right)$

$x - 4 y = 1 \to \left(2\right)$

$\text{from equation "(1)" we can express y in terms of x}$

$\Rightarrow y = 3 - 3 x \to \left(3\right)$

$\textcolor{b l u e}{\text{Substitute "y=3-3x" into equation }} \left(2\right)$

$x - 4 \left(3 - 3 x\right) = 1$

$\Rightarrow x - 12 + 12 x = 1$

$\Rightarrow 13 x - 12 = 1$

$\text{add 12 to both sides}$

$13 x \cancel{- 12} \cancel{+ 12} = 1 + 12$

$\Rightarrow 13 x = 13 \Rightarrow x = 1$

$\text{Substitute "x=1" into equation } \left(3\right)$

$\Rightarrow y = 3 - 3 = 0$

$\text{solution is } \left(x , y\right) \to \left(1 , 0\right)$