Chapter 11.1, Problem 42AYU

To determine

To find: The solution of the given system of equations.

Answer to Problem 42AYU

$x=-3,y=2,z=1$

Explanation of Solution

Given:

$2x+y=-4$

$-2y+4z=0$

$3x-2z=-11$

Calculation:

The system of equations is:

$2x+y=-4$

$-2y+4z=0$

$3x-2z=-11$

From the first equation we get,

$y=-4-2x$

Substituting $y=-4-2x$ in the second equation we get,

$-2\left(-4-2x\right)+4z=0$

$8+4x+4z=0$

$2+x+z=0$

$z=-2-x$

Substituting $z=-2-x$ in the third equation we get,

$3x-2\left(-2-x\right)=-11$

$3x+4+2x=-11$

$5x=-11-4$

$5x=-15$

$x=-\frac{15}{5}$

$x=-3$

Substituting $x=-3$ in the expression for $y=-4-2x$ we get,

$y=-4-2\left(-3\right)$

$y=-4+6$

$y=2$

Substituting $x=-3$ in the expression for $z=-2-x$ we get,

$z=-2-\left(-3\right)$

$z=-2+3$

$z=1$

Thus $x=-3,y=2,z=1$ is the solution of the given system of equations.