Question

error analysis jake was asked to estimate the solution of the system of equations. he incorrectly said the solution is (-1, -0.5). estimate the solution of the system by graphing the equations. what mistake might jake have made?
y - 2x = 0
y = 4x + 1
use the graphing tool to graph the system.
click to enlarge graph

Explanation:

Step1: Rewrite Equations

First, rewrite the equations in slope - intercept form ($y = mx + b$). The first equation $y - 2x=0$ can be rewritten as $y = 2x$. The second equation is already in slope - intercept form: $y=4x + 1$.

Step2: Find Intersection

To find the solution of the system

$$\begin{cases}y = 2x\\y=4x + 1\end{cases}$$

, set the two equations equal to each other: $2x=4x + 1$. Subtract $4x$ from both sides: $2x-4x=1$, so $- 2x=1$, and $x=-\frac{1}{2}=-0.5$. Then substitute $x = - 0.5$ into $y = 2x$, we get $y=2\times(-0.5)=-1$. So the correct solution is $(-0.5,-1)$.

Step3: Analyze Jake's Mistake

Jake said the solution was $(-1,-0.5)$. It seems that he mixed up the $x$ - coordinate and the $y$ - coordinate of the solution. He might have taken the $x$ - value from one equation's calculation and the $y$ - value from another in a wrong way, or misread the coordinates of the intersection point on the graph, swapping the $x$ and $y$ values.

Answer:

Jake likely mixed up the x - coordinate and y - coordinate of the solution. The correct solution is $(-0.5, - 1)$, while Jake gave $(-1, - 0.5)$, showing a swap of the x and y values.