In Exercises 19–30, solve each system by the addition method. x + 2y = 2 - 4x + 3y = 25

검증된 단계별 안내

Step 1: Multiply the first equation by 4 to align the coefficients of x.

Step 2: Add the modified first equation to the second equation to eliminate x.

Step 3: Solve the resulting equation for y.

Step 4: Substitute the value of y back into the original first equation.

Step 5: Solve for x.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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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 method requires manipulating the equations so that the coefficients of one variable are opposites, allowing for straightforward elimination.

Solving for Variables

After eliminating one variable, the resulting single-variable equation can be solved using basic algebraic techniques. Substituting this solution back into one of the original equations allows for finding the value of the other variable, completing the solution to the system.