Question

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
$y = -x + 2$
$x - 3y = -18$

Explanation:

Step1: Solve the system of equations

We have the system:

$$
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$$

Substitute \(y = -x + 2\) into the second equation:

$$ x - 3(-x + 2) = -18 $$

Step2: Simplify and solve for \(x\)

Expand the left - hand side:

$$ x + 3x-6=-18 $$

Combine like terms:

$$ 4x-6 = - 18 $$

Add 6 to both sides:

$$ 4x=-18 + 6=-12 $$

Divide both sides by 4:

$$ x=\frac{-12}{4}=-3 $$

Step3: Solve for \(y\)

Substitute \(x = - 3\) into \(y=-x + 2\):

$$ y=-(-3)+2=3 + 2 = 5 $$

So the solution to the system of equations is the point \((-3,5)\). To graph the lines:

• For \(y=-x + 2\), when \(x = 0\), \(y = 2\); when \(y = 0\), \(x=2\). Plot the points \((0,2)\) and \((2,0)\) and draw the line.
• For \(x - 3y=-18\), we can rewrite it as \(y=\frac{1}{3}x + 6\). When \(x = 0\), \(y = 6\); when \(y = 0\), \(x=-18\). Plot the points \((0,6)\) and \((-18,0)\) (but since our graph has a limited range, we can use the point we found from the solution \((-3,5)\) and another point, for example, when \(x = 3\), \(y=\frac{1}{3}(3)+6=7\), plot \((3,7)\) and draw the line. Then mark the point \((-3,5)\) as the solution.

Answer:

The solution to the system of equations is the point \((-3,5)\), and the two lines \(y=-x + 2\) and \(y=\frac{1}{3}x + 6\) (rewritten from \(x - 3y=-18\)) intersect at \((-3,5)\). When graphing, mark the point \((-3,5)\) as the solution.