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Graph the intersection or union, as appropriate, of the solutions of the pair of linear inequalities.

[tex]\[ 4x - y \geq 4 \][/tex]
[tex]\[ y \ \textless \ 2 \][/tex]

Use the graphing tool on the right to graph the solution. Click to enlarge the graph.

Sagot :

GinnyAnswer
To graph the system of inequalities \( 4x - y \geq 4 \) and \( y < 2 \), let's follow a detailed step-by-step approach.

### Step 1: Rewrite the Inequalities
1. For the first inequality \( 4x - y \geq 4 \):
- Rearrange it to solve for \( y \):
[tex]\[ 4x - y \geq 4 \implies y \leq 4x - 4 \][/tex]
- This represents a line \( y = 4x - 4 \) with a shaded region below or on the line.

2. For the second inequality \( y < 2 \):
- This inequality is already solved for \( y \):
[tex]\[ y < 2 \][/tex]
- This represents a horizontal line \( y = 2 \) with a shaded region below the line.

### Step 2: Identify the Boundary Lines
1. Boundary for the first inequality:
- Line equation: \( y = 4x - 4 \).

2. Boundary for the second inequality:
- Line equation: \( y = 2 \).

### Step 3: Graph the Boundary Lines
1. Graph \( y = 4x - 4 \):
- To plot this line, find two points:
- When \( x = 0 \):
[tex]\[ y = 4(0) - 4 = -4 \implies (0, -4) \][/tex]
- When \( x = 1 \):
[tex]\[ y = 4(1) - 4 = 0 \implies (1, 0) \][/tex]
- Draw the line through these points. Since the inequality is \( \geq \), the line will be solid.

2. Graph \( y = 2 \):
- This is a horizontal line passing through \( y = 2 \).
- Draw a dashed line (since the inequality is \( < \)) for \( y = 2 \).

### Step 4: Shade the Feasible Region
1. For \( y \leq 4x - 4 \):
- Shade the region below or on the solid line \( y = 4x - 4 \).

2. For \( y < 2 \):
- Shade the region below the dashed line \( y = 2 \).

### Step 5: Determine the Intersection
- The solution to the system of inequalities is the region where the shaded areas overlap. This gives us the final feasible region.

### Step 6: Final Graph
- The intersection of the two shaded regions is the feasible region bounded by \( y = 4x - 4 \) and below \( y = 2 \).

### Summary of the Boundary Equations
- \( 4x - y - 4 = 0 \) which simplifies to \( y = 4x - 4 \).
- \( y = 2 \).

By following these steps, you should be able to graph the system of inequalities [tex]\( 4 x - y \geq 4 \text{ and } y < 2 \)[/tex] and identify the feasible region which satisfies both inequalities.
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