Question

graph the system below and write its solution.\

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

\text{note that you can also answer
o solution\ or \infinitely many\}\text{solution: }

Explanation:

Step1: Simplify the first equation

We start with the equation \(6x + 2y=-6\). Divide every term by 2 to simplify it:
\[
\frac{6x}{2}+\frac{2y}{2}=\frac{-6}{2}
\]
Which simplifies to:
\[
3x + y=-3
\]
Now, solve for \(y\):
\[
y=-3x - 3
\]

Step2: Compare the two equations

The second equation is \(y = - 3x-1\). The first simplified equation gives \(y=-3x - 3\). These are two linear equations in slope - intercept form (\(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept). The slopes (\(m=-3\)) of both lines are the same, but the y - intercepts (\(b=-3\) for the first line and \(b = - 1\) for the second line) are different.
When two lines have the same slope but different y - intercepts, they are parallel lines. Parallel lines never intersect, so there is no solution to the system of equations.

Answer:

No solution