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Ch. 5 - Systems of Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 5 - Systems of Equations and InequalitiesProblema 5
Capitolo 6, Problema 5

In Exercises 5–18, solve each system by the substitution method. x + y = 4 y = 3x
Exercise 5: Solve the system of equations x + y = 4 and y = 3x using substitution.

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Start with the given system of equations: x+y=4y=3x.
Since the second equation already expresses y in terms of x as y = 3x, substitute this expression for y into the first equation.
After substitution, the first equation becomes x + 3x = 4. Combine like terms on the left side to simplify the equation.
Solve the simplified equation for x by isolating the variable.
Once you find the value of x, substitute it back into the expression y = 3x to find the corresponding value of y.

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System of Linear Equations

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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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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 effectively.
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