Question

graph the system below and write its solution.\

$$\begin{cases}y = -\\dfrac{1}{2}x - 1 \\\\ 2x + y = -4\\end{cases}$$

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

Explanation:

Step1: Solve the second equation for y

We have the equation \(2x + y = -4\). To solve for \(y\), we subtract \(2x\) from both sides.
\(y = -2x - 4\)

Step2: Set the two equations equal

We have \(y = -\frac{1}{2}x - 1\) and \(y = -2x - 4\). Since both equal \(y\), we set them equal to each other:
\(-\frac{1}{2}x - 1 = -2x - 4\)

Step3: Solve for x

First, add \(2x\) to both sides:
\(-\frac{1}{2}x + 2x - 1 = -4\)
\(\frac{3}{2}x - 1 = -4\)
Then add 1 to both sides:
\(\frac{3}{2}x = -4 + 1\)
\(\frac{3}{2}x = -3\)
Multiply both sides by \(\frac{2}{3}\):
\(x = -3\times\frac{2}{3}\)
\(x = -2\)

Step4: Find y

Substitute \(x = -2\) into the first equation \(y = -\frac{1}{2}x - 1\):
\(y = -\frac{1}{2}(-2) - 1\)
\(y = 1 - 1\)
\(y = 0\)

Answer:

The solution to the system is \(x = -2\), \(y = 0\) or \((-2, 0)\)