Chapter 3: Q4. (page 128)

Solve each system of inequalities. Sketch each graph on a sheet of paper.
4. $\begin{array}{l} y \geq x + 2 \\ y \leq - 2 x - 1 \end{array}$

Short Answer

Expert verified

The shaded region is the solution of the given inequations which is unbounded.

Step by step solution

Step-1 –Apply the concept of linear equation to solve the linear inequalities

We have,

$y = x + 2$

If $x = 1$ , then $y = 3 .$ .

If $x = 2$ , then $y = 4 .$ .

If $x = 3$ , then $y = 5 .$

$∴$ The points are $(1, 3), (2, 4)$ and $(3, 5) .$

For, $y = - 2 x - 1$

If $x = 1$ , then $y = - 2 (1) - 1$

$y = - 3 .$

If $x = 2$ , then $y = - 2 (2) - 1$ .

$\begin{array}{l} y = - 4 - 1 \\ = - 5. \end{array}$

If $x = 0$ , then $y = - 2 (3) - 1$

$y = - 7 .$

$∴$ The points are $(1, - 3), (2, - 5)$ and $(3, - 7) .$

Step-2–Plot the point on the graph paper and form a region of each inequation

Step-3–Identifying the common region

Since, the solution of $y \geq x + 2$ is away from the origin and the solution of $y \leq - 2 x - 1$ is also away from the region. Therefore, the shaded region is the common region that is the solution of inequation.

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Solve each system of inequalities. Sketch each graph on a sheet of paper.
4. $\begin{array}{l} y \geq x + 2 \\ y \leq - 2 x - 1 \end{array}$

Short Answer

Step by step solution

Step-1 –Apply the concept of linear equation to solve the linear inequalities

Step-2–Plot the point on the graph paper and form a region of each inequation

Step-3–Identifying the common region

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Solve each system of inequalities. Sketch each graph on a sheet of paper.4.y≥x+2y≤-2x-1

Short Answer

Step by step solution

Step-1 –Apply the concept of linear equation to solve the linear inequalities

Step-2–Plot the point on the graph paper and form a region of each inequation

Step-3–Identifying the common region

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Pure Maths

Applied Mathematics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve each system of inequalities. Sketch each graph on a sheet of paper.
4. $\begin{array}{l} y \geq x + 2 \\ y \leq - 2 x - 1 \end{array}$