Chapter 3: Q7. (page 128)

Solve each system of inequalities. Sketch each graph on a sheet of paper.
$\begin{array}{l} 6 y + 4 x \geq 12 \\ 5 y - 3 x \leq - 10 \end{array}$

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,

$6 y + 4 x = 12 .$

If $y = 0$ , then $x = 3$ .

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

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

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

For, $5 y - 3 x = - 10 .$

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

If $x = 5$ , then $y = 1$ .

If $y = 4$ , then $x = 10 .$

$∴$ The points are $(0, - 2), (5, 1)$ and $(10, 4) .$

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 $6 y + 4 x \geq 12$ is away from the origin and the solution of $5 y - 3 x \leq - 10$ is also away from 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.
$\begin{array}{l} 6 y + 4 x \geq 12 \\ 5 y - 3 x \leq - 10 \end{array}$

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.6y+4x≥125y-3x≤-10

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

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Study anywhere. Anytime. Across all devices.

Solve each system of inequalities. Sketch each graph on a sheet of paper.
$\begin{array}{l} 6 y + 4 x \geq 12 \\ 5 y - 3 x \leq - 10 \end{array}$