Question

Solve the system of linear equations by graphing.
`y = (3)/(4) x -4`
`y = - (1)/(2) x + 11`

Answer 1

Let's begin by listing out the information given to us:

`\begin{gathered} y=(3)/(4)x-4 \\ y=-(1)/(2)x+11 \end{gathered}`

We will proceed by graphing the functions, we have:

`\begin{gathered} We\text{ will make a table for these functions} \\ y=(3)/(4)x-4 \\ x=-2 \\ y=(3)/(4)(-2)-4=-1.5-4=-5.5_{} \\ (x,y)=(-2,-5.5) \\ x=0 \\ y=(3)/(4)(0)-4=0-4=-4 \\ x=4 \\ y=(3)/(4)(4)-4=3-4=-1 \\ \\ y=-(1)/(2)x+11 \\ x=-4 \\ y=-(1)/(2)(-4)+11=2+11=13 \\ x=0 \\ y=-(1)/(2)(0)+11=0+11=11 \\ x=8 \\ y=-(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}`

The solution is given by the point of intersection of the two functions (12, 5)