Question

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$$\begin{cases} y = \\frac{4}{3}x + 4 \\\\ 3y = -2x - 6 \\end{cases}$$

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use the mark feature tool to indicate the solution to the system on the graph.

Explanation:

⚡ Using what you learned: solving systems by graphing

Step 1: Rewrite the second equation in slope-intercept form

The system of equations is:

$$
LATEXBLOCK0
$$

Divide both sides of the second equation by \(3\):

$$ y = -\frac{2}{3}x - 2 $$

Step 2: Find the intersection point by setting the equations equal

$$ \frac{4}{3}x + 4 = -\frac{2}{3}x - 2 $$

Add \(\frac{2}{3}x\) to both sides:

$$ 2x + 4 = -2 $$

Subtract \(4\) from both sides:

$$ 2x = -6 $$

$$ x = -3 $$

Step 3: Solve for \(y\)

Substitute \(x = -3\) into the first equation:

$$ y = \frac{4}{3}(-3) + 4 = -4 + 4 = 0 $$

The solution to the system is the point \((-3, 0)\).

Answer:

The solution to the system is the point \((-3, 0)\). You should place the mark on the graph at the coordinates \((-3, 0)\).