Questions: Graph the system of inequalities. 3x - 2y ≤ 6 x - 1 > 0

Transcript text: Graph the system of inequalities. \[ \begin{array}{l} 3 x-2 y \leq 6 \\ x-1>0 \end{array} \]

Solution

Step 1: Rewrite the Inequalities in Slope-Intercept Form

For the inequality \(3x - 2y \leq 6\): \[ 3x - 2y \leq 6 \implies -2y \leq -3x + 6 \implies y \geq \frac{3}{2}x - 3 \]
For the inequality \(x - 1 > 0\): \[ x - 1 > 0 \implies x > 1 \]

Step 2: Graph the Boundary Lines

Graph the line \(y = \frac{3}{2}x - 3\). Since the inequality is \(y \geq \frac{3}{2}x - 3\), use a solid line and shade above the line.
Graph the line \(x = 1\). Since the inequality is \(x > 1\), use a dashed line and shade to the right of the line.

Step 3: Identify the Solution Region