Question

Solve the system by graphing:$\left\{\begin{array}{l}y=-\frac{1}{4}x+2\\ x+4y=-8\end{array}\right.$

Short answer

The system of equations $\left\{\begin{array}{l}y=-\frac{1}{4}x+2\\ x+4y=-8\end{array}\right.$has no solution and it can be seen in the graph as,

Step-by-step solution

Step 1. Given Information.

We are given a system of equations$\left\{\begin{array}{l}y=-\frac{1}{4}x+2\\ x+4y=-8\end{array}\right.$ and we need to find its solution by graphing.

Step 2. Graph the first equation.

The equation $y=-\frac{1}{4}x+2$is in slope-intercept form, so its slope is $-\frac{1}{4}$and its $y$intercept is $2$.

So its graph is given as

Step 3. Graph the second equation on the same rectangular coordinate system.

Solving the equation $x+4y=-8$for $y$we get,

localid="1644386022551" $\begin{array}{rcl}x+4y-x& =& -8-x\\ 4y& =& -x-8\\ \frac{4y}{4}& =& \frac{-x-8}{4}\\ y& =& -\frac{1}{4}x-2\end{array}$

So the slope of the line is $-\frac{1}{4}$and its $y$intercept is 2.

So the graph can be drawn on the same plane as,

Step 4. Identify the solution to the system.

• From the graph, it can be seen that the lines are parallel.
• Since no point is on both lines, there is no ordered pair that makes both equations true.
• There is no solution to the given system.