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Ch. 5 - Systems of Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Blitzer 8th EditionCh. 5 - Systems of Equations and Inequalities문제 2
6장, 문제 2

Determine whether the given ordered pair is a solution of the system. (−3,5)(- 3, 5)
{9x+7y=88x−9y=−69\(\begin{cases}\) 9x + 7y = 8 \\ 8x - 9y = -69 \(\end{cases}\)

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1
Identify the ordered pair given: \((-3, 5)\), where \(x = -3\) and \(y = 5\).
Substitute \(x = -3\) and \(y = 5\) into the first equation \(9x + 7y = 8\) to check if the equation holds true.
Calculate the left side of the first equation: \(9(-3) + 7(5)\) and compare it to the right side, which is \(8\).
Substitute \(x = -3\) and \(y = 5\) into the second equation \(8x - 9y = -69\) to check if this equation is also satisfied.
Calculate the left side of the second equation: \(8(-3) - 9(5)\) and compare it to the right side, which is \(-69\). If both equations are true, then the ordered pair is a solution to the system.

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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. The solution to the system is the set of values that satisfy all equations simultaneously. Understanding how to work with systems is essential for determining if a given ordered pair is a solution.
추천 영상:
4:27
Introduction to Systems of Linear Equations

Ordered Pair as a Solution

An ordered pair (x, y) is a solution to a system if substituting x and y into each equation makes both equations true. This involves replacing variables with the given values and verifying the equality holds for each equation.
추천 영상:
05:28
Equations with Two Variables

Substitution and Verification

Substitution involves plugging the values of x and y from the ordered pair into each equation. Verification means checking if the resulting expressions on both sides of the equation are equal, confirming whether the ordered pair satisfies the system.
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Solving Systems of Equations - Substitution
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