Questions: y - axis: 0 x - axis: 0 10 8 6 4 2 0 -2 -4 -6 -8 -6 -4 -2 0 2 4 6 8 10 x

Transcript text: y - axis: 0 x - axis: 0 $\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline 10 & & & & & & & & & & \\ \hline 8 & & & & & & & & & & \\ \hline 6 & & & & & & & & & & \\ \hline 4 & & & & & & & & & & \\ \hline 2 & & & & & & & & & & \\ \hline 0 & & & & & & & & & & \\ \hline -2 & & & & & & & & & & \\ \hline -4 & & & & & & & & & & \\ \hline -6 & & & & & & & & & & \\ \hline \end{array}$ $\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline -8 & -6 & -4 & -2 & 0 & 2 & 4 & 6 & 8 & 10 & x \\ \hline \end{array}$

Solution

Solution Steps

Step 1: Rewrite the equations in slope-intercept form.

The first equation $y - 4x = 0$ can be rewritten as $y = 4x$. The second equation is already in slope-intercept form: $y = 8x - 2$.

Step 2: Identify the slope and y-intercept of each equation.

For the equation $y = 4x$, the slope is 4 and the y-intercept is 0.

For the equation $y = 8x - 2$, the slope is 8 and the y-intercept is -2.

Step 3: Plot the lines on the graph.

For $y = 4x$, start at the origin (0,0) and use the slope of 4 (rise 4, run 1) to plot additional points. Draw a line through these points.

For $y = 8x - 2$, start at the y-intercept (0, -2) and use the slope of 8 (rise 8, run 1) to plot additional points. Draw a line through these points.

Step 4: Estimate the solution.

The solution to the system of equations is the point where the two lines intersect. Observing the graph (not provided), the intersection point appears to be approximately (0.5, 2).

Final Answer

The estimated solution is $\boxed{(0.5, 2)}$.

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