Chapter 11.1, Problem 11AYU

To determine

The solution of the given system of equations.

Answer to Problem 11AYU

Solution:

  $(x,y)=(4,1)$ 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,

  $\frac{1}{2}(3+y)+y=3$

  $\frac{3}{2}+\frac{1}{2}y+y=3$

  $\frac{3}{2}y=3-\frac{3}{2}$

  $\frac{3}{2}y=\frac{3}{2}$

  $y=1$

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 (4,1) satisfies the given system of equations and hence is the solution.