Solve each problem. See Examples 5 and 9. The sum of two numbers is 47, and the difference between the numbers is 1. Find the numbers.

검증된 단계별 안내

Let the two numbers be represented as \(x\) and \(y\).

Write the system of equations based on the problem statement: \(x + y = 47\) and \(x - y = 1\).

Add the two equations to eliminate \(y\): \((x + y) + (x - y) = 47 + 1\) which simplifies to \(2x = 48\).

Solve for \(x\) by dividing both sides of the equation by 2: \(x = \frac{48}{2}\).

Substitute the value of \(x\) back into one of the original equations (for example, \(x + y = 47\)) to solve for \(y\).

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.

Systems of Linear Equations

A system of linear equations consists of two or more linear equations with the same variables. Solving the system means finding values for the variables that satisfy all equations simultaneously. In this problem, the sum and difference of two numbers form a system that can be solved together.

Setting Up Equations from Word Problems

Translating a word problem into mathematical equations involves identifying variables and expressing relationships described in words as algebraic equations. Here, the sum and difference statements translate into two equations involving the two unknown numbers.

Solving Systems by Addition or Substitution

Common methods to solve systems include addition (elimination) and substitution. Addition involves adding or subtracting equations to eliminate a variable, while substitution solves one equation for a variable and substitutes into the other. Both methods help find the values of the unknown numbers.