Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}3y>x+2\\ -2x+6y>8\end{array}\right.$

Short answer

The solution of the equation is dark shaded region.

Step-by-step solution

Given information.  

Given system of equation,

$\left\{\begin{array}{l}3y>x+2\\ -2x+6y>8\end{array}\right.$

Graph the system of equations. 

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

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

$0>2$

which holds false.

Calculating for second equation.  

For $-2x+6y=8$,

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

we get

$0>8$,

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

Plotting the graph.