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

Feb 21, 2016

color(blue)(x=3, y=5)

#### Explanation:

we can use,

-$\textcolor{b l u e}{S u b s t i t u t i o n M e t h o d}$

Solving,

$\textcolor{red}{x + 2 y = 13}$
as equation(1)

$\textcolor{red}{3 x - y = 4}$
as equation(2)

first we must get the value of $x$ in equation(1), using algebraic techniques (isolating the variable $x$), we get:

$\textcolor{red}{x = 13 - 2 y}$
as equation(3)

substitute equation(3) to equation(2) to eliminate $x$,

$3 \left(13 - 2 y\right) - y = 4$

$39 - 6 y - y = 4$ (Combine like terms to simplify)

$39 - 7 y = 4$

$- 7 y = 4 - 39$

$- 7 y = - 35$

$y = \frac{- 35}{-} 7$

$\textcolor{b l u e}{y = 5}$

substitute $y$ to either equation(1) or equation(2) to get the final value of variable $x$

Substituting $y$ to Equation(1),

$x + 2 y = 13$

$x + 2 \left(5\right) = 13$

$x + 10 = 13$

$x = 13 - 10$

$\textcolor{b l u e}{x = 3}$