Chapter 11.1, Problem 24AYU

To determine

To find: The solution of the given system of equations.

Answer to Problem 24AYU

$x=-\frac{5}{3},y=1$

Explanation of Solution

Given:

$2x+4y=\frac{2}{3}$

$3x-5y=-10$

Calculation:

The system of equations is,

$2x+4y=\frac{2}{3}$

$3x-5y=-10$

Multiplying the first equation by 5 and the second equation by 4 and then adding these two we get,

$5\left(2x+4y\right)+4\left(3x-5y\right)=5\left(\frac{2}{3}\right)+4\left(-10\right)$

$10x+20y+12x-20y=\frac{10}{3}-40$

$22x=-\frac{110}{3}$

$x=-\frac{110}{3\left(22\right)}$

$x=-\frac{5}{3}$

Substituting $x=-\frac{5}{3}$ in the first equation we get,

$2\left(-\frac{5}{3}\right)+4y=\frac{2}{3}$

$-\frac{10}{3}+4y=\frac{2}{3}$

$4y=\frac{2}{3}+\frac{10}{3}$

$4y=\frac{12}{3}$

$4y=4$

$y=\frac{4}{4}$

$y=1$

Thus $x=-\frac{5}{3},y=1$ is the solution of the given system of equations.

The graph is as follows: