Question

4.1Error Analysis Jake was asked to estimate the solution of the system ofequations. He incorrectly said the solution is (-3, -1.5). Estimate the solution ofthe system by graphing the equations. What mistake might Jake have made?y-2x = 0y = 4x + 3Use the graphing tool to graph the system.Click toenlargegraph

Answer 1

The given system is-

`\mleft\{\begin{aligned}y-2x=0 \\ y=4x+3\end{aligned}\mright.`

We have to graph these equations. Remember that each equation represents a straight line. The image below shows both lines.

The important thing here is that the solution of the system is the common point of the lines.

Therefore, the solution is (-1.5, 3).

As you can observe, Jake's mistake was that he confused the coordinates, he wrote down inversely.-

On the other hand, to graph a linear equation we need just two points when x = 0, and y = 1. Let's the two points for the first equation y - 2x = 0.

For x = 0

`\begin{gathered} y-2x=0 \\ y-2(0)=0 \\ y=0 \end{gathered}`

So, the first point is (0,0).

Let's find the second point when y = 1.

`\begin{gathered} y-2x=0 \\ 1-2x=0 \\ -2x=-1 \\ x=(1)/(2) \end{gathered}`

The second point is the same (1/2,0).

Once you have the two points of the line, you draw them on the coordinated plane then you draw a straight line across those points. The image below shows this.

Then, you do the same process to graph the second equation to have the two lines as the first image shows.