Question

y = -3x + 3; 6x + 2y = 6; solution: handwritten steps; graph grid

Explanation:

Step1: Substitute y into the equation

Substitute $y=-3x+3$ into $6x+2y=6$:
$6x + 2(-3x+3) = 6$

Step2: Expand and simplify the left side

Distribute and combine like terms:
$6x -6x +6 = 6$
$6=6$

Step3: Interpret the result

The equation simplifies to a true statement with no variables, meaning the two equations represent the same line, so there are infinitely many solutions.

Step4: Graph the line

For $y=-3x+3$, find intercepts:

• When $x=0$, $y=3$ (y-intercept: $(0,3)$)
• When $y=0$, $0=-3x+3 \implies x=1$ (x-intercept: $(1,0)$)

Plot these points and draw a straight line through them; this line represents both equations.

Answer:

The system has infinitely many solutions, and the graph is the line $y=-3x+3$ passing through $(0,3)$ and $(1,0)$.