Question

graph the system below and write its solution.\

$$\begin{cases} y = -3x + 1 \\\\ -6x - 2y = 0 \\end{cases}$$

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

Explanation:

Step1: Simplify the second equation

We have the second equation \(-6x - 2y = 0\). Let's solve for \(y\) to get it in slope - intercept form (\(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept).
First, add \(6x\) to both sides: \(-2y=6x\). Then divide both sides by \(-2\): \(y = - 3x\).

Step2: Compare the slopes and y - intercepts

The first equation is \(y=-3x + 1\), which has a slope \(m_1=-3\) and a y - intercept \(b_1 = 1\).
The second equation (after simplification) is \(y=-3x\), which has a slope \(m_2=-3\) and a y - intercept \(b_2=0\).

Since the slopes of the two lines are equal (\(m_1 = m_2=-3\)) and the y - intercepts are different (\(b_1
eq b_2\)), the two lines are parallel. Parallel lines do not intersect, so the system of equations has no solution.

Answer:

No solution