Question

graph the system below and write its solution. \\(\

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

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

Explanation:

Step1: Rewrite the second equation

Let's rewrite the second equation \(-x - 3y = 6\) in slope - intercept form (\(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept).
First, we solve for \(y\):

$$
LATEXBLOCK0
$$

Step2: Compare the two equations

The first equation is \(y =-\frac{1}{3}x-3\) and the second equation (after re - writing) is \(y=-\frac{1}{3}x - 2\).
For a linear equation \(y = mx + b\), the slope \(m\) of the first equation is \(-\frac{1}{3}\) and the slope of the second equation is also \(-\frac{1}{3}\). But the y - intercepts are different (\(b_1=-3\) for the first equation and \(b_2 = - 2\) for the second equation).
If two lines have the same slope but different y - intercepts, they are parallel lines and parallel lines never intersect. So, the system of equations has no solution.

Answer:

No solution