Chapter 11.1, Problem 10AYU

To determine

The solution of the given system of equations.

Answer to Problem 10AYU

Solution:

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

Explanation of Solution

Given:

  $2x+\frac{1}{2}y=0$

  $3x-4y=-\frac{19}{2}$

  $x=-\frac{1}{2},y=2$

Calculation:

The system of equations is,

  $2x+\frac{1}{2}y=0$

  $3x-4y=-\frac{19}{2}$

From the first equation we get.

  $\frac{1}{2}y=-2x$

  $y=-4x$

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

  $3x-4(-4x)=-\frac{19}{2}$

  $3x+16x=-\frac{19}{2}$

  $19x=-\frac{19}{2}$

  $x=-\frac{1}{2}$

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

  $2\left(-\frac{1}{2}\right)+\frac{1}{2}y=0$

  $-1+\frac{1}{2}y=0$

  $\frac{1}{2}y=1$

  $y=2$

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

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