Question

graph the system below and write its solution.\

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

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note that you can also answer
o solution\ or \infinitely many\ solutions.

Explanation:

Step1: Rewrite the first equation

Let's rewrite the first equation \(x - 3y=-3\) in slope - intercept form (\(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept).
Start with \(x-3y=-3\). Subtract \(x\) from both sides: \(-3y=-x - 3\). Then divide each term by \(-3\): \(y=\frac{1}{3}x + 1\).

Step2: Compare the two equations

The second equation is already in slope - intercept form: \(y=\frac{1}{3}x + 1\).
We can see that both equations have the same slope (\(m=\frac{1}{3}\)) and the same y - intercept (\(b = 1\)). This means that the two lines are coincident (they lie on top of each other).

Answer:

Infinitely many solutions