# How do you solve the system of equations algebraically 8x-z=4, y+z=5, 11x+y=15?

Dec 13, 2016

$\left\{x = - \frac{6}{7} , y = \frac{111}{7} , z = - \frac{76}{7}\right\}$

#### Explanation:

$\text{given :}$

$8 x - z = 4 \text{ } \left(1\right)$

$y + z = 5 \text{ } \left(2\right)$

$x + y = 15 \text{ } \left(3\right)$

$\text{first find (2)-(3)}$

$\cancel{y} + z - x - \cancel{y} = 5 - 15$

$z - x = - 10 \text{ (4)}$

$\text{now find (1)+(4)}$

$8 x - \cancel{z} + \cancel{z} - x = 4 - 10$

$8 x - x = - 6$

$7 x = - 6$

$x = - \frac{6}{7}$

$\text{use (3)}$

$- \frac{6}{7} + y = 15$

$y = 15 + \frac{6}{7}$

$y = \frac{111}{7}$

$\text{use (2)}$

$\frac{111}{7} + z = 5$

$z = 5 - \frac{111}{7}$

$z = \frac{35 - 111}{7}$

$z = - \frac{76}{7}$