Question

graph the system below and write its solution.\

$$\begin{cases} y = -2x - 2 \\\\ -4x - 2y = 4 \\end{cases}$$

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

Explanation:

Step1: Simplify the second equation

We start with the second equation \(-4x - 2y = 4\). Let's solve for \(y\) to see if it matches the first equation. First, add \(4x\) to both sides: \(-2y = 4x + 4\). Then divide both sides by \(-2\): \(y=\frac{4x + 4}{-2}=-2x - 2\).

Step2: Compare the two equations

The first equation is \(y = -2x - 2\) and the second equation, after simplification, is also \(y = -2x - 2\). This means the two equations represent the same line. When two equations in a system represent the same line, there are infinitely many solutions because every point on the line is a solution to both equations.

Answer:

Infinitely many