Explanation Given: The sum of x -variable and y -variable is at most 3. The sum of y -variable to the product of 4 and the x -variable does not exceed 6. Method used: Graphing a Linear Inequality in Two Variables: 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation. Draw a solid line if the original inequality contains a ≥ or ≤ symbol. Draw a dashed line if the original inequality contains a > or < symbol. 2. Choose a test point from one of the half–planes. (Do not choose a point on the line.) Substitute the coordinates of the test point into inequality. 3. If a true statement results, shade the half-plane containing this test point. If a false statement results, shade the half-plane not containing this test point. Calculation: The given inequalities are x − y ≥ − 1 and 5 x − 2 y ≤ 10 . To sketch the graph of the solution set of the above system, first sketch the graph of each inequality. Use the above method and obtain the graph of the each inequality is as follows. The graph of the inequality x − y ≥ − 1 and 5 x − 2 y ≤ 10 is as follows. Step 1: Replace the inequality symbol by = and graph the linear equation: That is, replace the symbol ≤ and ≥ by = , and graph the linear equations x − y = − 1 and 5 x − 2 y = 10 . Use the intercepts concept to graph the line x − y = − 1 . To find x -intercept: Set y = 0 . x − y = − 1 x − 0 = − 1 x = − 1 Since, the x -intercept is − 1 , the graph will pass through ( − 1 , 0 ) . To find y -intercept: Set x = 0 . x − y = − 1 0 − y = − 1 y = 1 Since, the y -intercept is 1, the graph will pass through ( 0 , 1 ) . That is, the graph of x − y = − 1 will pass through the points ( − 1 , 0 ) and ( 0 , 1 ) . Similarly, the graph of 5 x − 2 y = 10 will pass through the points ( 2 , 0 ) and ( 0 , − 5 ) . Use the above intercepts and draw the graph of the line x − y = − 1 and 5 x − 2 y = 10 as a solid line as shown below in Figure 1. From Figure 1, it is observed that the both lines passes through a common point ( 4 , 5 ) . Step 2: Choose a test point from one of the half–planes. (Do not choose a point on the line.) Substitute the coordinates of the test point into inequality. The line x − y = − 1 divides the x y -plane into three parts, namely the line itself and the two half-planes. The test point in one half-plane satisfy x − y ≤ − 1 and the test point in other half-plane satisfy x − y ≥ − 1 . To find the half-plane to which the solution of x − y ≥ − 1 belong s, choose a test point ( 0 , 0 ) from either of the half-planes

College Algebra Essentials (5th Edition)

5th Edition

ISBN: 9780134469294

Author: Blitzer, Robert F.

Publisher: PEARSON

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Chapter 5.5, Problem 72E

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To sketch: The graph of the union of inequalities x−y≥−1 and 5x−2y≤10.

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Chapter 5.5, Problem 71E

Chapter 5.5, Problem 73E

Chapter 5 Solutions

College Algebra Essentials (5th Edition)

Ch. 5.1 - Consider the system: {2x3y=42x+y=4. Determine if...Ch. 5.1 - Prob. 2CP Ch. 5.1 - Prob. 3CP Ch. 5.1 - Prob. 4CP Ch. 5.1 - Solve the system: {5x2y=410x+4y=7.Ch. 5.1 - Prob. 6CP Ch. 5.1 - Prob. 7CP Ch. 5.1 - Prob. 8CP Ch. 5.1 - Prob. 1CVC Ch. 5.1 - Prob. 2CVC

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The graph of the union of inequalities x − y ≥ − 1 and 5 x − 2 y ≤ 10 .

Solution Summary: The author explains how to sketch the graph of the union of inequalities x-yge -1 and 5x-2y

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To sketch: The graph of the union of inequalities x−y≥−1 and 5x−2y≤10.

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Chapter 5 Solutions