Chapter 11: Q. 54 (page 783)

In Problems 53–56, write a system of linear inequalities for the given graph.
54.

Short Answer

Expert verified

The inequalities are

$\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x \leq 6 \\ y \leq 5 \\ x + y \geq 2 \end{cases}$

Step by step solution

Step 1. Given information

The graph is in first quadrant so the values are $x \geq 0$ & $y \geq 0$

Step 2. About parallel lines

The lines parallel to y-axis has equation $x = k$

here $k = 6$ then the equation is $x = 6$

the lines parallel to x-axis has equation $y = k$

here k=5 then the equation is $y = 5$

Due to origin not included in the region so the inequalities are $x \leq 6$ & $y \leq 5$

Step 3. About line equation of given points

Given the points are $(0, 2)$ & $(2, 0)$

slope: $m = (\frac{y_{2} - y_{1}}{(x_{2} - x 1)}$

$m = \frac{(2 - 0)}{(0 - 2)} m = - 1$

The line equation is:

$y - y_{1} = m (x - x_{1}) y - 0 = - 1 (x - 2) y = - x + 2 x + y = 2$

The line excludes the origin so the inequality $x + y \geq 2$ .

Atep 4. Solution

The inequalities bounded by the given graph

$\{\begin{cases} x \geq 0 \\ y \geq 0 \\ x \leq 6 \\ y \leq 5 \\ x + y \geq 2 \end{cases}$

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In Problems 53–56, write a system of linear inequalities for the given graph.
54.

Short Answer

Step by step solution

Step 1. Given information

Step 2. About parallel lines

Step 3. About line equation of given points

Atep 4. Solution

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In Problems 53–56, write a system of linear inequalities for the given graph.54.

Short Answer

Step by step solution

Step 1. Given information

Step 2. About parallel lines

Step 3. About line equation of given points

Atep 4. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Mechanics Maths

Logic and Functions

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 53–56, write a system of linear inequalities for the given graph.
54.