Question

Can someone please help me solve and graph this equation?

Answer 1

We have the following system:

`\begin{cases}y=3x-8 \\ x+4y=20\end{cases}`

Each one of those equations represents a line, and their interception is the solution for this system(if the lines are parallel, there's no solution, and if they are the same line, infinite solutions).

We can calculate their interception, by making a substitution. Using the value for 'y' from the first equation in the second equation, we get the following:

`\begin{gathered} \begin{cases}y=3x-8 \\ x+4y=20\end{cases}\Rightarrow x+4(3x-8)=20 \\ \Rightarrow x+12x-32=20 \\ 13x=52 \\ x=(52)/(13)=4 \end{gathered}`

Using our 'x' value in any of those equations, we get our interception.

`y(4)=3(4)-8=12-8=4`

The solution for this system is

`\begin{gathered} \begin{cases}x=4 \\ y=4\end{cases} \\ (4,4) \end{gathered}`

To plot those lines, you just need two points of each line. Since (4,4) is the interception, it belongs to both lines, then, we just need an extra point from each one. An easy point to calculate is the y-intercept.

Calculating the y-intercept for the first line:

`y=3(0)-8=-8`

y-intercept = (0,-8)

Calculating the x-intercept for the second line:

`0+4y=20\Rightarrow y=5`

y-intercept = (0,5)

To plot, you just mark the y-intercept and drag to the point (4,4).

The graphs looks like this: