Chapter 11.1, Problem 10AYU

To determine

The solution of the given system of equations.

Answer to Problem 10AYU

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

Explanation of Solution

Given:

$2x\text{ + }\frac{1}{2}y=\text{ 0}$

$3x-4y=-\frac{19}{2}$

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

Calculation:

The system of equations is,

$2x\text{ + }\frac{1}{2}y=\text{ 0}$

$3x-4y=-\frac{19}{2}$

From the first equation we get,

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

$y=-4x$

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

$3x-4\left(-4x\right)=-\frac{19}{2}$

$3x+16x=-\frac{19}{2}$

$19x=-\frac{19}{2}$

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

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.