# How do you use substitution or elimination to solve the system of equations? 2x-3y-z=0, 3x+2y+2z=2, and x+5y+3z=2

Dec 6, 2017

The given system of eqns. has infinitely many solutions.

#### Explanation:

Name the given eqns. $2 x - 3 y - z = 0. \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \left\langle1\right\rangle .$

$3 x + 2 y + 2 z = 2. \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \left\langle2\right\rangle .$

$x + 5 y + 3 z = 2. \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \left\langle3\right\rangle .$

Observe that, adding $\left\langle1\right\rangle \mathmr{and} \left\langle3\right\rangle , \text{ we get } \left\langle2\right\rangle .$

Therefore, the given system of eqns. has infinitely many solns.