Question

graph the system of inequalities.
x + y > 7
2x - 3y < 6
note: after you make your two linear inequalities, use the red and blue buttons in the bottom right of the graph to ensure you correctly have a solid or dashed line. after you are satisfied with the lines, place a green dot representing the correct shaded region on the graph by clicking the graph.

Explanation:

Step1: Rewrite to slope-intercept form

For $x + y > 7$:
$y > -x + 7$
For $2x - 3y < 6$:
$-3y < -2x + 6$
$y > \frac{2}{3}x - 2$ (reverse inequality when dividing by negative)

Step2: Identify line type

Both inequalities use $>$, so dashed lines for $y = -x + 7$ and $y = \frac{2}{3}x - 2$ (dashed because the boundary is not included).

Step3: Graph boundary lines

• $y = -x + 7$: y-intercept $(0,7)$, slope $-1$ (goes down 1, right 1)
• $y = \frac{2}{3}x - 2$: y-intercept $(0,-2)$, slope $\frac{2}{3}$ (goes up 2, right 3)

Step4: Shade correct region

For $y > -x + 7$, shade above its dashed line.
For $y > \frac{2}{3}x - 2$, shade above its dashed line.
The overlapping shaded region is the solution set; place a green dot in this overlapping area (e.g., the point $(6,3)$ which satisfies both inequalities: $6+3=9>7$ and $2(6)-3(3)=12-9=3<6$).

Answer:

1. Draw a dashed line for $y = -x + 7$ (y-intercept (0,7), slope -1)
2. Draw a dashed line for $y = \frac{2}{3}x - 2$ (y-intercept (0,-2), slope $\frac{2}{3}$)
3. Shade the region that is above both dashed lines, and place a green dot in this overlapping area (e.g., at $(6,3)$)