Chapter 11.1, Problem 42AYU

To determine

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

Answer to Problem 42AYU

Solution:

  $x=-3,y=2,z=1$

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,

  $-2(-4-2x)+4z=0$

  $8+4x+4z=0$

  $2+x+z=0$

  $z=-2-x$

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

  $3x-2(-2-x)=-11$

  $3x+4+2x=-11$

  $5x=-11-4$

  $5x=-15$

  $x=-\frac{15}{5}$

  $x=-3$

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

  $y=-4-2(-3)$

  $y=-4+6$

  $y=2$

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

  $z=-2-(-3)$

  $z=-2+3$

  $z=1$

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