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 27

6장, 문제 27

In Exercises 19–30, solve each system by the addition method. 3x - 4y = 11 2x + 3y = - 4

검증된 단계별 안내

Step 1: Write down the system of equations clearly:

3x - 4 y = 11 2 x + 3 y = - 4

Step 2: To use the addition method, multiply each equation by a suitable number so that the coefficients of either

x

y

are opposites. For example, multiply the first equation by 3 and the second equation by 4 to align the coefficients of

y

3(3x - 4y) = 3(11) and 4(2x + 3y) = 4(-4)

Step 3: After multiplication, the system becomes:

9x - 12y = 33 and 8x + 12y = -16

. Now add the two equations to eliminate

y

(9x - 12y) + (8x + 12y) = 33 + (-16)

Step 4: Simplify the resulting equation to solve for

x

. Once you find

x

, substitute it back into one of the original equations to solve for

y

Step 5: Write the solution as an ordered pair

(x, y)

representing the values of

x

and

y

that satisfy both equations.

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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.

Addition (Elimination) Method

The addition method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable. This requires manipulating the equations, often by multiplying by constants, to align coefficients for elimination.

Solving for Variables After Elimination

Once a variable is eliminated, the resulting single-variable equation is solved using basic algebra. After finding one variable, substitution back into one of the original equations allows solving for the other variable, completing the solution to the system.