Ch. 5 - Systems of Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

Blitzer 8th Edition

Ch. 5 - Systems of Equations and Inequalities

문제 11

6장, 문제 11

In Exercises 5–18, solve each system by the substitution method. 5x + 2y = 0 x - 3y = 0

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Start with the given system of equations:

5x + 2 y = 0 x - 3 y = 0

Solve one of the equations for one variable in terms of the other. For example, from the second equation

x - 3 y = 0

, solve for

x

x = 3 y

Substitute the expression for

x

from step 2 into the first equation: replace

x

with

3 y

5x + 2y = 0

to get

5(3y) + 2y = 0

Simplify the resulting equation and solve for

y

15y + 2y = 0

which simplifies to

17y = 0

, then solve for

y

Use the value of

y

found in step 4 and substitute it back into the expression for

x

from step 2 to find the value of

x

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주요 개념

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

System 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 represent these systems is fundamental to solving them.

Substitution Method

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation. This reduces the system to a single equation with one variable, making it easier to solve step-by-step.

Solving Linear Equations

Solving linear equations requires isolating the variable using algebraic operations such as addition, subtraction, multiplication, and division. Mastery of these operations is essential to find the exact values of variables in the system.