교과서 질문
In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. 3x+y≤6, 2x−y≤−1, x>−2, y<4
585
views
Ch. 5 - Systems of Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
당신이 사용하는 게 아니라요?교과서 변경다른 교과서를 선택하세요
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 59
Exercises 57–59 will help you prepare for the material covered in the next section. Solve:
검증된 단계별 안내1
Identify the system of equations given:
\(A + B = 3\),
\(2A - 2B + C = 17\),
\(4A - 2C = 14\).
From the first equation, express one variable in terms of the other. For example, solve for \(B\):
\(B = 3 - A\).
Substitute the expression for \(B\) into the second equation to eliminate \(B\):
\(2A - 2(3 - A) + C = 17\).
Simplify the second equation after substitution to get an equation in terms of \(A\) and \(C\) only.
Use the third equation \(4A - 2C = 14\) along with the simplified second equation to solve the system of two equations with two variables (\(A\) and \(C\)). Then back-substitute to find \(B\).
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
5m도움이 되었나요?
주요 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 goal is to find values for the variables that satisfy all equations simultaneously. Methods such as substitution, elimination, or matrix operations are commonly used to solve these systems.
추천 영상:
4:27
Introduction to Systems of Linear Equations
Substitution and Elimination Methods
Substitution involves solving one equation for a variable and substituting that expression into other equations. Elimination involves adding or subtracting equations to eliminate one variable, simplifying the system. Both methods help reduce the system to fewer variables for easier solving.
추천 영상:
6:04How to Multiply Equations in Elimination Method
Manipulating and Combining Equations
Solving systems often requires multiplying or dividing entire equations to align coefficients, enabling elimination of variables. Careful manipulation preserves equality and simplifies the system step-by-step. This skill is essential for efficiently solving multi-variable linear systems.
추천 영상:
5:22Combinations
관련 실천
교과서 질문
Write the given sentences as a system of inequalities in two variables. Then graph the system. The sum of the x-variable and the y-variable is at most 4. The y-variable added to the product of 3 and the x-variable does not exceed 6.
573
views
교과서 질문
In Exercises 63–64, write each sentence as an inequality in two variables. Then graph the inequality. The y-variable is at least 4 more than the product of -2 and the x-variable.
632
views
교과서 질문
Graph the solution set of each system of inequalities or indicate that the system has no solution.
375
views
교과서 질문
In Exercises 57–59, graph the region determined by the constraints. Then find the maximum value of the given objective function, subject to the constraints. This is a piecewise function. Refer to the textbook.
581
views
교과서 질문
Exercises 57–59 will help you prepare for the material covered in the next section. Add: (5x−3)/(x2+1) + 2x/(x2+1)2.
675
views