# How do you solve this set of linear equations: 3x + 2y + 6= - 17+ 7y - x; 3x + x = y + 5?

Jun 20, 2018

color(maroon)(x = 3, y = 7

#### Explanation:

$3 x + 2 y + 6 = - 17 + 7 y - x$

$4 x - 5 y = - 23 , \text{ Eqn (1)}$

$3 x + x = y + 5$

$4 x - y = 5 , \text{ Eqn (2)}$

Subtracting Eqn (1) from Eqn (2),

$\cancel{4 x} - y - \cancel{4 x} + 5 y = 5 + 23$

4y = 28 ' or " y = 7#

Substituting the value of y in Eqn (2),

$4 x - 7 = 5$

$x = \frac{5 + 7}{4} = 3$