Q 17. - Intermediate Algebra

Question

In the following exercises, solve the following system of equations by graphing.

$\left\{\begin{array}{l}-2x+4y=4\\ y=\frac{1}{2}x\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the system $\left\{\begin{array}{l}-2x+4y=4\\ y=\frac{1}{2}x\end{array}\right.$has no solution. It is found by a graph as,

Step 1. Given information.

Consider the given system of linear equations,

$$\begin{gathered} -2x+4y=4 \\ y=\frac{1}{2}x \end{gathered}$$

Step 2. Solve the first equation for y.

Find the slope and y-intercept of the first equation.

$\begin{array}{rcl}-2x+4y& =& 4\\ 4y& =& 2x+4\\ y& =& \frac{1}{2}x+1\end{array}$

Here the slope is m=$\frac{1}{2}$ and, the y-intercept is b = 1.

Step 3. Solve the second equation for y , and find the slope and y -intercept.

Find the slope and y-intercept of the second equation.

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

Here the slope m=$\frac{1}{2}$and, the y-intercept is b=0.

Step 4. Graph both the lines.

The graph of both equation on one plane is drawn as,

The lines are parallel.

Since, no point in both lines, there is no ordered pair that makes both equations true.

Therefore, no solution to this system.