Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}y\le -\frac{1}{2}x+3\\ y<1\end{array}\right.$

Short answer

In the following exercises, solve each system by graphing.

Step-by-step solution

Given information   

Given system of equation

$\left\{\begin{array}{l}y\le -\frac{1}{2}x+3\\ y<1\end{array}\right.$

Graph the system of equations   

The system of equations $y=-\frac{1}{2}x+3$has intercept $x=6,y=3$.The boundary is solid. Origin lies within.

Calculating for second equation   

For $y<1$, the intercepts are $x=0,y=1$and testing the point $(0,0)$, we get

$0<1$which is true hence, origin is contained in it.

Plotting the graph