Question

graph the system below and write its solution.\

$$\begin{cases}-x - 3y = -6 \\\\ y = -\\dfrac{1}{3}x + 2\\end{cases}$$

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

Explanation:

Step1: Rewrite the first equation

Start with \(-x - 3y = -6\). Let's solve for \(y\) to see its slope - intercept form (\(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept).
Add \(x\) to both sides: \(-3y=x - 6\).
Divide each term by \(-3\): \(y=-\frac{1}{3}x + 2\).

Step2: Compare the two equations

The second equation is already in slope - intercept form: \(y =-\frac{1}{3}x+2\).
We can see that both equations are identical. This means that the two lines represented by the equations are the same line.

Answer:

Infinitely many solutions