Chapter 11.1, Problem 11AYU

To determine

The solution of the given system of equations.

Answer to Problem 11AYU

$\left(x,y\right)=\left(4,\text{ 1}\right)$ is the solution.

Explanation of Solution

Given:

$x-y=3$

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

$x=4,y=1$

Calculation:

The system of equations is,

$x-y=3$

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

From the first equation we get,

$x=3+y$

Substituting this value of $x$ in the second equation we get,

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

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

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

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

$y=1$

Substituting this value of $y$ in the first equation we get,

$x-1=3$

$x=3+1$

$x=4$

Thus the solution is $x=4,y=1$.

Therefore the given point $\left(4,\text{ 1}\right)$ satisfies the given system of equations and hence is the solution.