# How do you solve the system x+y-z=2, 3x+5y-2z=-5, and 5x+4y-7z=-7?

Sep 5, 2016

The soln. : $x = 30 , y = - 13 , z = 15$.

#### Explanation:

Let us solve the system of eqns. using Elimination Method.

From the First eqn., $z = x + y - 2$

Using this $z$ in the second and the third eqns., we get,

$3 x + 5 y - 2 \left(x + y - 2\right) = - 5 \text{, i.e., } x + 3 y = - 9$

$5 x + 4 y - 7 \left(x + y - 2\right) = - 7 \text{, or, } - 2 x - 3 y = - 21$

Adding these last eqns., $x = 30$.

Then from, $x + 3 y = - 9 , y = - 13$.

Finally, $z = x + y - 2 = 15$.

These roots satisfy the given eqns.

The soln. : $x = 30 , y = - 13 , z = 15$.