Chapter 11.1, Problem 34AYU

To determine

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

Answer to Problem 34AYU

$x=2,y=-3$

Explanation of Solution

Given:

$\frac{1}{2}x+y=-2$

$x-2y=8$

Calculation:

The system of equations is:

$\frac{1}{2}x+y=-2$

$x-2y=8$

Multiplying the first equation by 2 and then adding to the second equation we get,

$2\left(\frac{1}{2}x+y\right)+\left(x-2y\right)=2\left(-2\right)+8$

$x+2y+x-2y=-4+8$

$2x=4$

$x=\frac{4}{2}$

$x=2$

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

$2-2y=8$

$-2y=8-2$

$-2y=6$

$y=\frac{6}{-2}$

$y=-3$

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