Question

Graph the system x+y=8 and 6x+3y=36

Answer 1

Let's conside the first equation x+y=8

Since it is an equation with degree 1, it is a straight line. So 2 coordinates are enough to plot a graph.

To plot a grpah, let's take, x=0,1

If x=0

`\begin{gathered} x+y=8 \\ 0+y=8 \\ y=8 \end{gathered}`

So, the coordinate is (0,8)

If x=1

`\begin{gathered} 1+y=8 \\ y=8-1 \\ y=7 \end{gathered}`

So, the coordinated is (1,7)

Let's plot the graph.

Let's take the second equation

6x+3y=36

If x=0

`\begin{gathered} 6x+3y=36 \\ 0+3(y)=36 \\ y=(36)/(3) \\ y=9 \end{gathered}`

Hence the y coordinated is (0,9)

If x=1

`\begin{gathered} 6x+3y=36 \\ 6(1)+3y=36 \\ 3y=36-6 \\ y=(30)/(10) \\ y=10 \end{gathered}`

Hence the coordinate is (1,10)

Let's plot the graph

Hence both the graphs are plotted.