Question

for each system, choose the best description of its solution. if the system has exactly one solution, give its solution. (a) \

$$\begin{cases} \\text{line 1: } & y = -x - 3 \\\\ \\text{line 2: } & x + y = -3 \\end{cases}$$

describe the solution. \bigcirc the system has exactly one solution

Explanation:

Step1: Rewrite Line 2 to slope-intercept form

Starting with Line 2: $x+y=-3$, solve for $y$:
$y = -x - 3$

Step2: Compare the two equations

Line 1 is $y=-x-3$, Line 2 simplifies to the same equation. This means the two lines are identical, so every point on the line is a solution.

Answer:

The system has infinitely many solutions, all points on the line $y=-x-3$ (or $x+y=-3$)