Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}y\ge 3x-1\\ -3x+y>-4\end{array}\right.$

Short answer

The solution of the equation is dark shaded region.

Step-by-step solution

Given information.  

Given system of equation,

$\left\{\begin{array}{l}y\ge 3x-1\\ -3x+y>-4\end{array}\right.$

Graph the system of equations. 

The system of equation $y=3x-1$

has intercept $x=0.3,y=-1$. The boundary is solid. Origin does lies within as putting

$0\ge -1$

which holds true.

Calculating for second equation. 

For $-3x+y=4$,

the intercepts are $x=-1.3,y=4$testing the point $(0,0)$,

we get

$0>-4$,

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

Plotting the graph.