교과서 질문
In Exercises 47–52, solve each system by the method of your choice.
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Ch. 5 - Systems of Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
6장, 문제 48
In Exercises 47–48, solve each system by the method of your choice. (x - y)/3 = (x + y)/2 - 1/2 (x + 2)/2 - 4 = (y + 4)/3
검증된 단계별 안내1
Step 1: Start by rewriting each equation to eliminate the fractions. For the first equation, multiply both sides by the least common denominator (LCD) of 3 and 2, which is 6, to clear the denominators.
Step 2: After multiplying, simplify the resulting equation by distributing and combining like terms. This will give you a linear equation in terms of x and y without fractions.
Step 3: For the second equation, multiply both sides by the LCD of 2 and 3, which is 6, to clear the denominators. Then simplify by distributing and combining like terms.
Step 4: Now you have a system of two linear equations without fractions. Use either substitution or elimination method to solve for x and y. For elimination, align the equations and add or subtract them to eliminate one variable.
Step 5: Once one variable is eliminated, solve for the remaining variable. Substitute this value back into one of the original simplified equations to find the value of the other variable.
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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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7m주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Systems of Linear Equations
A system of linear equations consists of two or more linear equations with the same variables. The solution is the set of variable values that satisfy all equations simultaneously. Understanding how to interpret and manipulate these systems is essential for finding their solutions.
추천 영상:
4:27
Introduction to Systems of Linear Equations
Methods for Solving Systems
Common methods to solve systems include substitution, elimination, and graphing. Each method involves manipulating the equations to isolate variables or eliminate one variable, making it easier to find the solution. Choosing the appropriate method depends on the system's structure.
추천 영상:
04:03Choosing a Method to Solve Quadratics
Algebraic Manipulation and Simplification
Solving the given system requires careful algebraic manipulation, such as clearing denominators, combining like terms, and isolating variables. Simplifying complex fractions and expressions is crucial to transform the system into a more manageable form for solving.
추천 영상:
05:09Introduction to Algebraic Expressions
관련 실천
교과서 질문
In Exercises 49–50, solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0, b ≠ 0 5ax + 4y = 17 ax + 7y = 22
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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
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교과서 질문
Graph the solution set of each system of inequalities or indicate that the system has no solution.
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교과서 질문
In Exercises 47–52, solve each system by the method of your choice.
554
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교과서 질문
Graph the solution set of each system of inequalities or indicate that the system has no solution.
560
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