# How do you solve the following system: x+y=4 , 3x + 4y = 11 ?

$x = 5$, $y = - 1$

#### Explanation:

Given that

$x + y = 4 \setminus \ldots \ldots \ldots \left(1\right)$

$3 x + 4 y = 11 \setminus \ldots \ldots \ldots \left(2\right)$

Multiplying (1) by $3$ & subtracting from (2) as follows

$3 x + 4 y - 3 \left(x + y\right) = 11 - 3 \setminus \times 4$

$y = - 1$

setting $y = - 1$ in (1), we get

$x = 4 - y = 4 - \left(- 1\right) = 5$

hence, the solution is $x = 5$ & $y = - 1$