Chapter 11.1, Problem 27AYU

To determine

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

Answer to Problem 27AYU

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

Explanation of Solution

Given:

$2x-y=0$

$4x+2y=12$

Calculation:

The system of equations is,

$2x-y=0$

$4x+2y=12$

From the first equation we get,

$y=2x$

Substituting $y=2x$ in the second equation we get,

$4x+2\left(2x\right)=12$

$4x+4x=12$

$8x=12$

$x=\frac{12}{8}$

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

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

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

$3-y=0$

$y=3$

Thus $x=\frac{3}{2},y=3$ is the solution of the given system of equations.

The graph is as follows:

The graph of the given system of equations represents two lines $2x-y=0$ and $4x+2y=12$ intersecting at the point $\left(\frac{3}{2},3\right)$.