Chapter EP, Problem 3.1.6EP

To determine

Solve the given system of equation by graphing or making table

Answer to Problem 3.1.6EP

The given system of equation intersects at $\left(0,1\right)$ .

Explanation of Solution

Given information:

System of equation:

  $\begin{array}{l}y=\frac{1}{3}x+1\\ y=4x+1\end{array}$

Formula used:

A line can be plotted by knowing two points on line. To know these two points any one value from x or y is put on equation and other is obtained.

  $y=\frac{1}{3}x+1$

Putting $x=0$ ,

  $\begin{array}{l}y=\frac{1}{3}x+1\\ y=\frac{1}{3}\left(0\right)+1\\ y=1\end{array}$

First point is $\left(0,1\right)$

Putting $y=0$ ,

  $\begin{array}{l}y=\frac{1}{3}x+1\\ 0=\frac{1}{3}x+1\\ -1=\frac{1}{3}x\\ -3=x\end{array}$

second point is $\left(-3,0\right)$

The line $y=\frac{1}{3}x+1$ passes from $\left(-3,0\right)$ and $\left(0,1\right)$ ,

  $y=4x+1$

Putting $x=0$ ,

  $\begin{array}{l}y=4x+1\\ y=4\left(0\right)+1\\ y=1\end{array}$

First point is $\left(0,1\right)$

Putting $y=0$ ,

  $\begin{array}{l}y=4x+1\\ 0=4x+1\\ -1=4x\\ \frac{-1}{4}=x\end{array}$

second point is $\left(-\frac{1}{4},0\right)$

The line $\frac{2}{5}x-\frac{4}{3}y=-2$ passes from $\left(0,1\right)$ and $\left(-\frac{1}{4},0\right)$ ,

Now, plotting graphs with the points located on them,

The given system of equation intersects at $\left(0,1\right)$ .