Let's begin by listing out the information given to us:
[tex]\begin{gathered} y=\frac{3}{4}x-4 \\ y=-\frac{1}{2}x+11 \end{gathered}[/tex]We will proceed by graphing the functions, we have:
[tex]\begin{gathered} We\text{ will make a table for these functions} \\ y=\frac{3}{4}x-4 \\ x=-2 \\ y=\frac{3}{4}(-2)-4=-1.5-4=-5.5_{} \\ (x,y)=(-2,-5.5) \\ x=0 \\ y=\frac{3}{4}(0)-4=0-4=-4 \\ x=4 \\ y=\frac{3}{4}(4)-4=3-4=-1 \\ \\ y=-\frac{1}{2}x+11 \\ x=-4 \\ y=-\frac{1}{2}(-4)+11=2+11=13 \\ x=0 \\ y=-\frac{1}{2}(0)+11=0+11=11 \\ x=8 \\ y=-\frac{1}{2}(8)+11=-4+11=7 \\ \\ We\text{ will plot these points on a graph to obtain our solution as shown below} \end{gathered}[/tex]The solution is given by the point of intersection of the two functions (12, 5)
