Question

how many solutions are there to this system of linear equations? \\(\

$$\begin{cases} y = -4x - 1 \\\\ y = -4x - 1 \\end{cases}$$

\\) no solutions; one solution; an infinite number of solutions

Explanation:

Step1: Analyze the equations

The system is \(

$$\begin{cases}y = -4x - 1\\y = -4x - 1\end{cases}$$

\). Both equations are identical.

Step2: Recall solution types for linear systems

For two linear equations \(y = m_1x + b_1\) and \(y = m_2x + b_2\):

• If \(m_1

eq m_2\), there's one solution.

• If \(m_1 = m_2\) and \(b_1

eq b_2\), no solutions.

• If \(m_1 = m_2\) and \(b_1 = b_2\), infinite solutions (same line).

Here, \(m_1 = m_2=-4\) and \(b_1 = b_2=-1\), so they represent the same line.

Answer:

an infinite number of solutions