Chapter 3: Q6. (page 128)

Solve each system of inequalities. Sketch each graph on a sheet of paper.
2. $\begin{array}{l} y + 3 x \geq 6 \\ y - 2 x \leq 9 \end{array}$

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.

For, $y + 3 x = 6$

If $y = 0$ , then $x = 2$ .

If $x = 0$ , then $y = 6$ .

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

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

For, $y - 2 x = 9$

For, $x = - 2$

If $x = - 2$ , then $y = 5$ .

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

If $x = - 4$ , then $y = 1 .$

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

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 $y + 3 x \geq 6$ is away from the origin and the solution of $y - 2 x \leq 9$ is towards the normal. 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.
2. $\begin{array}{l} y + 3 x \geq 6 \\ y - 2 x \leq 9 \end{array}$

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.2.y+3x≥6y-2x≤9

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

Applied Mathematics

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Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Solve each system of inequalities. Sketch each graph on a sheet of paper.
2. $\begin{array}{l} y + 3 x \geq 6 \\ y - 2 x \leq 9 \end{array}$