Chapter 11.1, Problem 9AYU

To determine

The solution of the given system of equations.

Answer to Problem 9AYU

Solution:

  $(x,y)=\left(2,\frac{1}{2}\right)$ is the solution.

Explanation of Solution

Given:

  $3x-4y=4$

  $\frac{1}{2}x-3y=-\frac{1}{2}$

  $x=2,y=\frac{1}{2}$

Calculation:

The system of equations is,

  $3x-4y=4$

  $\frac{1}{2}x-3y=-\frac{1}{2}$

From the second equation we get,

  $\frac{1}{2}x=3y-\frac{1}{2}$

  $x=6y-1$

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

  $3(6y-1)-4y=4$

  $18y-3-4y=4$

  $14y=4+3$

  $14y=7$

  $y=\frac{7}{14}$

  $y=\frac{1}{2}$

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

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

  $x-3=-1$

  $x=-1+3$

  $x=2$

Thus the solution is $x=2,y=\frac{1}{2}$

Therefore the given point $\left(2,\frac{1}{2}\right)$ satisfies the given system of equations and hence is the solution.