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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 7
6장, 문제 7

In Exercises 5–18, solve each system by the substitution method. {x+3y=8y=2x−9\(\begin{cases}\) x + 3y = 8 \\ y = 2x - 9 \(\end{cases}\)

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Identify the system of equations: \(\begin{cases} x + 3y = 8 \\ y = 2x - 9 \end{cases}\).
Since the second equation is already solved for \(y\), substitute \(y = 2x - 9\) into the first equation.
Replace \(y\) in the first equation: \(x + 3(2x - 9) = 8\).
Simplify and solve the resulting equation for \(x\): \(x + 6x - 27 = 8\).
Once you find \(x\), substitute it back into \(y = 2x - 9\) to find the value of \(y\).

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주요 개념

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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 represent these systems is fundamental to solving them.
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4:27
Introduction to Systems of Linear Equations

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 especially useful when one equation is already solved for a variable.
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Choosing a Method to Solve Quadratics

Solving Linear Equations

Solving linear equations means finding the value(s) of the variable(s) that make the equation true. This often involves isolating the variable using inverse operations like addition, subtraction, multiplication, or division. Mastery of these techniques is essential for solving systems after substitution.
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Solving Linear Equations with Fractions
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