Chapter 11.1, Problem 38AYU

To determine

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

Answer to Problem 38AYU

$x=\frac{1}{2},y=\text{ 2}$

Explanation of Solution

Given:

$2x-y=-1$

$x+\frac{1}{2}y=\frac{3}{2}$

Calculation:

The system of equations is:

$2x-y=-1$

$x+\frac{1}{2}y=\frac{3}{2}$

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

$\left(2x-y\right)+2\left(x+\frac{1}{2}y\right)=-1+2\left(\frac{3}{2}\right)$

$2x-y+2x+y=-1+3$

$4x=2$

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

$x=\frac{1}{2}$

Substituting $x=\frac{1}{2}$ in the first equation we get,

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

$1-y=-1$

$-y=-1-1$

$-y=-2$

$y=\text{ 2}$

Thus $x=\frac{1}{2},y=\text{ 2}$ is the solution of the given system of equations.