Question

can you show me how to do this on the graph aswell

Answer 1

Solution:

The system of inequalities is given below as

$\begin{gathered} 3x+2y\leq6 \\ 4x-y\leq8 \end{gathered}$

Step 1:

Put x=0 and find y

$\begin{gathered} 3x+2y=6 \\ 3(0)+2y=6 \\ 2y=6 \\ \frac{2y}{2}=\frac{6}{2} \\ y=3 \\ (0,3) \end{gathered}$

Put y=0 and find x

$\begin{gathered} 3x+2y=6 \\ 3x+2(0)=6 \\ 3x=6 \\ \frac{3x}{3}=\frac{6}{3} \\ x=2 \\ (2,0) \end{gathered}$

Step 2:

Put x= 0 and find y

$\begin{gathered} 4x-y=8 \\ 4(0)-y=8 \\ -y=8 \\ y=-8 \\ (0,-8) \end{gathered}$

Put y=0 and find x

$\begin{gathered} 4x-y=8 \\ 4x-0=8 \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \\ (2,0) \end{gathered}$

By using a graphing calculator, we will have

THE PURPLE REGION IS THE REGION TO BE SHADED