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 15

6장, 문제 15

In Exercises 5–18, solve each system by the substitution method. 2x - 3y = 8 - 2x 3x + 4y = x + 3y + 14

검증된 단계별 안내

Step 1: Simplify each equation to standard form. For the first equation, combine like terms:

2x - 3 y = 8 - 2 x

becomes

2x + 2x - 3 y = 8

, which simplifies to

4 x - 3 y = 8

Step 2: Simplify the second equation similarly:

3 x + 4 y = x + 3 y + 14

becomes

3 x - x + 4 y - 3 y = 14

, which simplifies to

2 x + y = 14

Step 3: Solve one of the equations for one variable. For example, solve the second equation for

y

y = 14 - 2 x

Step 4: Substitute the expression for

y

from Step 3 into the first equation:

4 x - 3 (14 - 2 x) = 8

Step 5: Simplify and solve the resulting equation for

x

. Then, substitute the value of

x

back into the expression for

y

to find the value of

y

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

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 set of variables. The solution is the set of variable values that satisfy all equations simultaneously. Understanding how to interpret and manipulate these equations is essential for solving the system.

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. It is particularly useful when one variable is easily isolated.

Simplifying and Rearranging Equations

Before applying substitution, equations often need to be simplified and rearranged to isolate variables or combine like terms. This step ensures clarity and accuracy in substitution and helps avoid errors during solving. Mastery of algebraic manipulation is crucial here.