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Use the drawing tool(s) to form the correct answer on the provided graph.

Graph the following system of equations in the coordinate plane. Use the Mark Feature tool to indicate the solution to the system on the graph.

[tex]\[
\begin{array}{l}
y = -x + 2 \\
x - 3y = -18
\end{array}
\][/tex]

\begin{tabular}{|l|}
\hline
Drawing Tools \\
\hline
Select \\
\hline
Mark Feature \\
\hline
Line \\
\hline
\end{tabular}

Click on a tool to begin drawing.

Undo | Reset

Sagot :

GinnyAnswer
Let's solve the system of equations graphically and identify their point of intersection, which represents the solution to the system.

The system of equations is:
[tex]\[ \begin{array}{l} y = -x + 2 \\ x - 3y = -18 \end{array} \][/tex]

### Step-by-Step Graphing Instructions

1. Equation 1: [tex]\(y = -x + 2\)[/tex]
- This is a linear equation in slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
- The slope [tex]\(m = -1\)[/tex] and the y-intercept [tex]\(b = 2\)[/tex].
- Plot the y-intercept at point [tex]\((0, 2)\)[/tex].
- From [tex]\((0, 2)\)[/tex], use the slope to find another point. Since the slope is [tex]\(-1\)[/tex], go down 1 unit and right 1 unit to point [tex]\((1, 1)\)[/tex].
- Draw the line through these points.

2. Equation 2: [tex]\(x - 3y = -18\)[/tex]
- This needs to be converted to slope-intercept form [tex]\(y = mx + b\)[/tex].
- Solve for [tex]\(y\)[/tex] as follows:
[tex]\[ x - 3y = -18 \implies -3y = -x - 18 \implies y = \frac{1}{3}x + 6 \][/tex]
- The slope is [tex]\(\frac{1}{3}\)[/tex] and the y-intercept is [tex]\(6\)[/tex].
- Plot the y-intercept at point [tex]\((0, 6)\)[/tex].
- From [tex]\((0, 6)\)[/tex], use the slope to find another point. Since the slope is [tex]\(\frac{1}{3}\)[/tex], go up 1 unit and right 3 units to point [tex]\((3, 7)\)[/tex].
- Draw the line through these points.

3. Intersection Point
- The solution to the system is where the two lines intersect.
- Upon plotting both lines on the same coordinate plane, identify their intersection point.

From the solution provided, the intersection occurs at [tex]\((-3, 5)\)[/tex]. This point should be clearly marked on the graph.

### Summary

- For the line [tex]\(y = -x + 2\)[/tex], plot points [tex]\((0, 2)\)[/tex] and [tex]\((1, 1)\)[/tex].
- For the line [tex]\(y = \frac{1}{3}x + 6\)[/tex], plot points [tex]\((0, 6)\)[/tex] and [tex]\((3, 7)\)[/tex].
- Mark the intersection point at [tex]\((-3, 5)\)[/tex].

This intersection represents the solution to the system of equations, which is [tex]\((-3, 5)\)[/tex].

Now you can use the provided drawing and marking tools to graph these lines and indicate the solution [tex]\((-3, 5)\)[/tex] on your coordinate plane.
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