Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}y\ge -3x+2\\ 3x+y>5\end{array}\right.$

Short answer

The solution of the equation is the dark shaded region.

Step-by-step solution

Given information.   

Given system of equation,

$\left\{\begin{array}{l}y\ge -3x+2\\ 3x+y>5\end{array}\right.$

Graph the system of equations   

The system of equation $y=-3x+2$

has intercept $x=0.6,y=2$. The boundary is solid. Origin does not lies within as putting

$$\begin{gathered} (0,0) \\ 0\ge 2 \end{gathered}$$

which holds false.

Calculating for second equation 

For $3x+y=5$,

the intercepts are $x=1.6,y=5$and testing the point ,

we get

$0>5$,

which is false hence, the origin is not contained in it.

Plotting the graph.