Questions: Solve the system of linear inequalities graphically by matching the solution region with one of the four regions shown in the multiple choice. -3x + y ≥ 6 x ≤ 3

Solution Steps

The inequality $-3x + y \ge 6$ can be rewritten as $y \ge 3x + 6$.

The line $y=3x+6$ has a y-intercept of 6 and a slope of 3. The line $x=3$ is a vertical line passing through x=3.

For $y \ge 3x+6$, the shaded region is above the line $y=3x+6$. For $x \le 3$, the shaded region is to the left of the line $x=3$. The solution region is the intersection of these two shaded regions.

Final Answer: The correct answer is B.