How do solve the following linear system?:  3x - y = -6, 4x+3y=29 ?

Dec 11, 2017

color(red)[(x = 11/13) and (y = 111/13) OR

We can simplify the fractions and write the solutions as

color(red)[(x ~~ 0.8) and (y ~~ 8.5)

Explanation:

We are given the linear systems of equations given below:

$3 x - y = - 6$ $\textcolor{b l u e}{E q n .1}$

$4 x + 3 y = 29$ $\textcolor{b l u e}{E q n .2}$

Multiply $\textcolor{b l u e}{E q n .1}$ by $3$

Hence, $\textcolor{b l u e}{E q n .1}$ yields $\textcolor{b l u e}{E q n .3}$

$9 x - 3 y = - 18$ $\textcolor{b l u e}{E q n .3}$

$4 x + 3 y = 29$ $\textcolor{b l u e}{E q n .2}$

When we add $\textcolor{b l u e}{E q n .3}$ and $\textcolor{b l u e}{E q n .2}$ we get

$9 x - \cancel{3 y} = - 18$ $\textcolor{b l u e}{E q n .3}$
$4 x + \cancel{3 y} = 29$ $\textcolor{b l u e}{E q n .2}$

$\Rightarrow 13 x = 11$

Therefore, $\textcolor{red}{x = \frac{11}{13}}$

Substitute this value of $\textcolor{red}{x}$ in $\textcolor{b l u e}{E q n .1}$

$3 x - y = - 6$ $\textcolor{b l u e}{E q n .1}$

$\Rightarrow 3 \left(\frac{11}{13}\right) - y = - 6$

$\Rightarrow \left(\frac{33}{13}\right) - y = - 6$

$\Rightarrow - y = - 6 - \left(\frac{33}{13}\right)$

$\Rightarrow - y = \frac{- 78 - 33}{13}$

$\Rightarrow - y = - \frac{111}{13}$

Divide both sides by $- 1$ to get

$\Rightarrow y = \frac{111}{13}$

Hence, our final solutions are : -

color(red)[(x = 11/13) and (y = 111/13) OR

We can simplify the fractions and write the solutions as

color(red)[(x ~~ 0.8) and (y ~~ 8.5)