Question

1. a system of equations is shown.

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$$\begin{cases} \\frac{1}{3}x + 2y = -1 \\\\ y = \\frac{2}{3}x - 3 \\end{cases}$$

what is the x - value of the solution to the system of equations?
enter your answer in the box.

Explanation:

Step1: Substitute \( y \) into first equation

We know \( y = \frac{2}{3}x - 3 \), substitute it into \( \frac{1}{3}x + 2y = -1 \).
So we get \( \frac{1}{3}x + 2(\frac{2}{3}x - 3) = -1 \).

Step2: Simplify the equation

First, distribute the 2: \( \frac{1}{3}x + \frac{4}{3}x - 6 = -1 \).
Then combine like terms: \( \frac{1 + 4}{3}x - 6 = -1 \), which is \( \frac{5}{3}x - 6 = -1 \).

Step3: Solve for \( x \)

Add 6 to both sides: \( \frac{5}{3}x = -1 + 6 = 5 \).
Multiply both sides by \( \frac{3}{5} \): \( x = 5\times\frac{3}{5} = 3 \).

Answer:

3