Question

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

$$\begin{cases}y = -\\frac{3}{4}x - 6 \\\\ y = -\\frac{3}{4}x - 6\\end{cases}$$

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

Explanation:

Step1: Analyze the equations

The system of linear equations is \(

$$\begin{cases}y = -\frac{3}{4}x - 6\\y = -\frac{3}{4}x - 6\end{cases}$$

\). Both equations are identical.

Step2: Determine the number of solutions

For a system of linear equations \(y = m_1x + b_1\) and \(y = m_2x + b_2\), if \(m_1=m_2\) and \(b_1 = b_2\), the two lines are coincident (they lie on top of each other). When two lines are coincident, every point on one line is also on the other line, so there are an infinite number of solutions.

Answer:

an infinite number of solutions