Chapter 11.1, Problem 33AYU

To determine

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

Answer to Problem 33AYU

$x=\frac{3}{2},y=\text{ 1}$

Explanation of Solution

Given:

$2x+3y=6$

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

Calculation:

The system of equations is:

$2x+3y=6$

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

Multiplying the second equation by 3 and then adding to the first equation we get,

$\left(2x+3y\right)+3\left(x-y\right)=6+3\left(\frac{1}{2}\right)$

$2x+3y+3x-3y=6+\frac{3}{2}$

$5x=\frac{15}{2}$

$x=\frac{3}{2}$

Substituting $x=\frac{3}{2}$ in the second equation we get,

$\frac{3}{2}-y=\frac{1}{2}$

$-y=\frac{1}{2}-\frac{3}{2}$

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

$y=\text{ 1}$

Thus $x=\frac{3}{2},y=\text{ 1}$ is the solution of the given system of equations.