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Ch. 5 - Systems of Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Blitzer 8th EditionCh. 5 - Systems of Equations and Inequalities문제 47
6장, 문제 47

In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.



This

is a piecewise function. Refer to the textbook.

검증된 단계별 안내
1
Step 1: Begin by analyzing the system of inequalities provided in the problem. A system of inequalities typically consists of two or more inequalities that must be satisfied simultaneously. If the image is not visible, refer to the textbook for the specific inequalities.
Step 2: Rewrite each inequality in slope-intercept form (y = mx + b) if necessary. This makes it easier to graph the inequalities. For example, if an inequality is given as Ax + By ≤ C, solve for y to express it in terms of x.
Step 3: Graph each inequality on the coordinate plane. Use a solid line for inequalities that include equality (≤ or ≥) and a dashed line for strict inequalities (< or >). Shade the region that satisfies each inequality. The shading direction depends on the inequality sign: above the line for '>' or '≥', and below the line for '<' or '≤'.
Step 4: Identify the overlapping shaded region, which represents the solution set of the system of inequalities. If there is no overlapping region, the system has no solution.
Step 5: If the problem involves a piecewise function, graph each segment of the function separately based on its domain restrictions. Ensure that the graph accurately reflects the behavior of the function within each specified interval.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
6m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Systems of Inequalities

A system of inequalities consists of two or more inequalities that share the same variables. The solution set is the region where the graphs of these inequalities overlap. Understanding how to graph each inequality and identify the feasible region is crucial for solving these systems.
추천 영상:
6:19
Systems of Inequalities

Graphing Techniques

Graphing techniques involve plotting inequalities on a coordinate plane to visualize their solution sets. This includes determining boundary lines, using dashed or solid lines to indicate whether points on the line are included, and shading the appropriate regions. Mastery of these techniques is essential for accurately representing the solution set.
추천 영상:
02:16
Graphs and Coordinates - Example

Piecewise Functions

A piecewise function is defined by different expressions based on the input value. Understanding how to interpret and graph piecewise functions is important, as they can affect the boundaries of the solution set in a system of inequalities. Recognizing the conditions under which each piece applies is key to solving related problems.
추천 영상:
4:56
Function Composition
관련 실천
교과서 질문

In Exercises 47–52, solve each system by the method of your choice. {2x2+xy=6x2+2xy=0\(\begin{cases}\) 2x^2 + xy = 6 \\ x^2 + 2xy = 0 \(\end{cases}\)

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교과서 질문

In Exercises 47–48, solve each system by the method of your choice. (x + 2)/2 - (y + 4)/3 = 3 (x + y)/5 = (x - y)/2 - 5/2

864
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교과서 질문

Graph the solution set of each system of inequalities or indicate that the system has no solution.

{x2+y2≤16x+y>2\(\begin{cases}\) x^2 + y^2 \(\leq\) 16 \\ x + y > 2 \(\end{cases}\)

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교과서 질문

In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.


This

is a piecewise function. Refer to the textbook.

577
views
교과서 질문

In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers. The difference between the squares of two numbers is 3. Twice the square of the first number increased by the square of the second number is 9. Find the numbers.

539
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교과서 질문

Perform each long division and write the partial fraction decomposition of the remainder term. (x4-x2+2)/(x3-x2)

753
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