Math / Geometry

QuestionSolve tile system of inequalitues by grapining. $\begin{array}{l} y \geq 2 \\ y<4 \end{array}$
Select a line to change it between solid and dotted. Select a region to shade it. $y \geq 2 \quad y<4$ shade

Studdy Solution

STEP 1

1. We are dealing with a system of linear inequalities.
2. The inequalities are in terms of $y$ and involve horizontal lines.
3. The solution requires graphing the inequalities on a coordinate plane.

STEP 2

1. Graph the line $y = 2$ and determine its style (solid or dotted).
2. Graph the line $y = 4$ and determine its style (solid or dotted).
3. Identify and shade the region that satisfies both inequalities.

STEP 3

Graph the line $y = 2$ :
- Since the inequality is $y \geq 2$ , the line $y = 2$ should be solid, indicating that points on the line are included in the solution set.

STEP 4

Graph the line $y = 4$ :
- Since the inequality is $y < 4$ , the line $y = 4$ should be dotted, indicating that points on the line are not included in the solution set.

STEP 5

Identify and shade the region that satisfies both inequalities:
- The region that satisfies $y \geq 2$ is above or on the line $y = 2$ . - The region that satisfies $y < 4$ is below the line $y = 4$ . - The overlapping region, which satisfies both inequalities, is between the solid line $y = 2$ and the dotted line $y = 4$ .
Shade this region to indicate the solution set.
The solution is the region between the lines $y = 2$ and $y = 4$ , including the line $y = 2$ but not including the line $y = 4$ .

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