Chapter 11.1, Problem 32AYU

To determine

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

Answer to Problem 32AYU

$x=\frac{1}{5},y=\frac{3}{10}$

Explanation of Solution

Given:

$3x-2y=0$

$5x+10y=4$

Calculation:

The system of equations is:

$3x-2y=0$

$5x+10y=4$

From the first equation we get,

$2y=3x$

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

Substituting $y=\frac{3}{2}x$ in the second equation we get,

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

$5x+15x=4$

$20x=4$

$x=\frac{4}{20}$

$x=\frac{1}{5}$

Substituting $x=\frac{1}{5}$ in the first equation we get,

$3\left(\frac{1}{5}\right)-2y=0$

$\frac{3}{5}-2y=0$

$2y=\frac{3}{5}$

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

$y=\frac{3}{10}$

Thus $x=\frac{1}{5},y=\frac{3}{10}$ is the solution of the given system of equations.