Question

Solve the following system of equations graphically on the set of axes below
\[
\begin{array}{c}
y=x-2 \\
y=-3 x-6
\end{array}
\]

Plot two lines by clicking the graph.
Click a line to delete it.
\[
{ }_{10}^{y}
\]

Step 1 ：Plot the first equation \(y = x - 2\). This is a straight line with a slope of 1 and a y-intercept of -2. Start at the point \((0, -2)\) on the y-axis. Since the slope is 1, move up one unit and to the right one unit to find the next point. Continue this pattern to draw the line.

Step 2 ：Plot the second equation \(y = -3x - 6\). This is a straight line with a slope of -3 and a y-intercept of -6. Start at the point \((0, -6)\) on the y-axis. Since the slope is -3, move down three units and to the right one unit to find the next point. Continue this pattern to draw the line.

Step 3 ：Find the point where the two lines intersect. This point is the solution to the system of equations. By looking at the graph, you can see that the lines intersect at the point \((2, 0)\).

Step 4 ：\(\boxed{x = 2}\) and \(\boxed{y = 0}\) are the solutions to the system of equations.