Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}y\le -\frac{1}{4}x-2\\ x+4y\le 6\end{array}\right.$

Short answer

The solution of the equation is dark shaded region.

Step-by-step solution

Given information.    

Given system of equation,

$\left\{\begin{array}{l}y\le -\frac{1}{4}x-2\\ x+4y\le 6\end{array}\right.$

Graph the system of equations.

The system of equation $y=-\frac{1}{4}x-2$

has intercept $x=-8,y=-2$. The boundary is solid. Origin does not lies within as putting

$0\le -2$

which holds false.

Calculating for second equation.

For $x+4y=6$,

the intercepts are $x=6,y=1.5$testing the point $(0,0)$,

we get

$0\le 6$,

which is true hence, the origin is contained in it.

Plotting the graph.