# How do you solve the following linear system: 4x+3y=8 , x-2y=13 ?

Jan 28, 2016

$\left(x , y\right) = \left(5 , - 4\right)$

#### Explanation:

$4 x + 3 y = 8$

$x - 2 y = 13$

In the second equation we can find the value of $x$ by transposing $2 y$ to the other side of the equation and we can substitute the value of $x$ to the other equation

Solve for second equation:

$\rightarrow x - 2 y = 13$

Add $2 y$ both sides:

$\rightarrow x = 13 + 2 y$

Substitute the value of $x$ to the first equation:

$\rightarrow 4 \left(13 + 2 y\right) + 3 y = 8$

$\rightarrow \left(52 + 8 y\right) + 3 y = 8$

$\rightarrow 52 + 8 y + 3 y = 8$

$\rightarrow 52 + 11 y = 8$

$\rightarrow 11 y = 8 - 52$

$\rightarrow 11 y = - 44$

$\rightarrow y = - \frac{44}{11} = - 4$

So,substitute value of y to second equation:

$\rightarrow x - 2 \left(- 4\right) = 13$

$\rightarrow x - \left(- 8\right) = 13$

$\rightarrow x + 8 = 13$

$\rightarrow x = 13 - 8 = 5$

So,$\left(x , y\right) = \left(5 , - 4\right)$