Q 314 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing. 

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

Step-by-Step Solution

Answer

The solution of the equation is dark shaded region.

Step 1: Given information.

Given system of equation, 

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

Step 2: 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.

Step 3: 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.

Step 4: Plotting the graph.