Question

graph the system of equations.
$3x + 3y = 6$
$y + 4 = -(x - 6)$

Explanation:

Step1: Rewrite first equation to slope-intercept form

Start with $3x + 3y = 6$. Divide all terms by 3:
$\frac{3x}{3} + \frac{3y}{3} = \frac{6}{3}$
Simplify to get $y = -x + 2$

Step2: Rewrite second equation to slope-intercept form

Start with $y + 4 = -(x - 6)$. Distribute the negative sign:
$y + 4 = -x + 6$
Subtract 4 from both sides:
$y = -x + 2$

Step3: Analyze the two equations

Both equations simplify to $y = -x + 2$, meaning they are the same line.

Step4: Match to the given graphs

The first graph shows a single line with y-intercept 2 and slope -1, which matches the equation.

Answer:

The correct graph is the top one (the single line with y-intercept at (0,2) and x-intercept at (2,0)).