Question

here is a system of equations.
\

$$\begin{cases} y = -3x - 2 \\\\ y = -x - 4 \\end{cases}$$

graph the system. then write its solution. note that you can also answer
o solution\ or \infinitely many\ solutions.

Explanation:

Step1: Set equations equal

$-3x - 2 = -x - 4$

Step2: Solve for $x$

$-3x + x = -4 + 2$
$-2x = -2$
$x = \frac{-2}{-2} = 1$

Step3: Find $y$ via substitution

Substitute $x=1$ into $y=-x-4$:
$y = -1 - 4 = -5$

Step4: Verify with first equation

Substitute $x=1$ into $y=-3x-2$:
$y = -3(1) - 2 = -5$

Answer:

The solution is the point $(1, -5)$

*(For graphing:

1. For $y=-3x-2$: plot the y-intercept $(0, -2)$, then use slope $-3$ to plot another point (e.g., $(1, -5)$) and draw the line.
2. For $y=-x-4$: plot the y-intercept $(0, -4)$, then use slope $-1$ to plot another point (e.g., $(1, -5)$) and draw the line.

The two lines intersect at $(1, -5)$.)*