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

Mar 25, 2018

$x = \frac{1}{2}$
$y = \frac{5}{2}$

#### Explanation:

Given -

$x + y = 3$
$3 x + y = 4$

$x + y = 3$ -------------(1)
$3 x + y = 4$-------------(2) -----(1) $-$(2)

$- 2 x = - 1$
$x = \frac{- 1}{- 2} = \frac{1}{2}$

Substitute $x = \frac{1}{2}$ in equation (1)

$\frac{1}{2} + y = 3$
$y = 3 - \frac{1}{2} = \frac{6 - 1}{2} = \frac{5}{2}$