Chapter 3: Q3. (page 128)

Solve each system of inequalities. Sketch each graph on a sheet of paper.
$\begin{array}{l} y \geq 1 - x \\ y \leq x + 5 \end{array}$

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 inequation.

We have,

$y = 1 - x$

If $x = 1$ , then $y = 0$ .

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

If $x = 0$ , then $y = 1 .$

$∴$ The points are $(1, 0), (2, - 1)$ and $(0, 1) .$

For, $y = x + 5$

If $x = 1$ , then $y = 6$ .

If $x = - 2$ , then $y = 3$ .

If $x = 0$ , then $y = 5 .$

$∴$ The points are $(1, 6), (- 2, 3)$ and $(0, 5) .$

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 $y \geq 1 - x$ is away from the origin and the solution of $y \leq x + 5$ is towards the origin. 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.
$\begin{array}{l} y \geq 1 - x \\ y \leq x + 5 \end{array}$

Short Answer

Step by step solution

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

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.y≥1-xy≤x+5

Short Answer

Step by step solution

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

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

Pure Maths

Discrete Mathematics

Calculus

Applied Mathematics

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve each system of inequalities. Sketch each graph on a sheet of paper.
$\begin{array}{l} y \geq 1 - x \\ y \leq x + 5 \end{array}$