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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 5 - Systems and MatricesProblem 9
Chapter 6, Problem 9

Solve each system by substitution.
x - 5y = 8
x = 6y

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1
Identify the two equations in the system: \(x - 5y = 8\) and \(x = 6y\).
Since the second equation already expresses \(x\) in terms of \(y\), substitute \(x = 6y\) into the first equation.
Replace \(x\) in the first equation with \$6y$ to get \(6y - 5y = 8\).
Simplify the equation to combine like terms: \((6y - 5y) = y\), so the equation becomes \(y = 8\).
Use the value of \(y\) found to substitute back into \(x = 6y\) to find the corresponding value of \(x\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Systems of Linear Equations

A system of linear equations consists of two or more linear equations with the same variables. The goal is to find values for the variables that satisfy all equations simultaneously. Solutions can be a single point, infinitely many points, or no solution.
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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.
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Solving Linear Equations

Solving linear equations means isolating the variable to find its value. This often involves operations like addition, subtraction, multiplication, or division to simplify the equation and solve for the unknown.
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Related Practice
Textbook Question

Find the dimension of each matrix. Identify any square, column, or row matrices.

[8−2463]\(\left\)[ \(\begin{matrix}\) 8 & -2 & 4 & 6 & 3 \(\end{matrix}\) \(\right\)]

Textbook Question

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix In.)

[5723]and[3−7−25]\(\left\)[ \(\begin{matrix}\) 5 & 7 \\2 & 3 \(\end{matrix}\) \(\right\)]\(\quad\) \(\text{and}\) \(\quad\]\left\)[ \(\begin{matrix}\) 3 & -7 \\-2 & 5 \(\end{matrix}\) \(\right\)]

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Textbook Question

Use the given row transformation to change each matrix as indicated.

[156−4−12371],4×row 1 added to row 2\(\left\)[ \(\begin{matrix}\) 1 & 5 & 6 \\ -4 & -1 & 2 \\ 3 & 7 & 1 \(\end{matrix}\) \(\right\)], \(\quad\) 4 \(\times\) \(\text{row 1 added to row 2}\)

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Textbook Question

Evaluate each determinant.

∣−1−253∣\(\left\)| \(\begin{matrix}\) -1 & -2 \\ 5 & 3 \(\end{matrix}\) \(\right\)|

Textbook Question

Use the given row transformation to change each matrix as indicated.

[156−23−1470],2×row 1 added to row 2\(\left\)[ \(\begin{matrix}\) 1 & 5 & 6 \\ -2 & 3 & -1 \\ 4 & 7 & 0 \(\end{matrix}\) \(\right\)], \(\quad\) 2 \(\times\) \(\text{row 1 added to row 2}\)

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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x + 2)/((x + 2)(2x - 1))

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