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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 17
Chapter 6, Problem 17

Solve each system by substitution.
3y = 5x + 6
x + y = 2

Verified step by step guidance
1
Start with the given system of equations: \(3y = 5x + 6\) and \(x + y = 2\).
Solve one of the equations for one variable. For example, solve the second equation for \(y\): \(y = 2 - x\).
Substitute the expression for \(y\) from the second equation into the first equation: \(3(2 - x) = 5x + 6\).
Simplify and solve the resulting equation for \(x\): distribute the 3 and combine like terms to isolate \(x\).
Once you find the value of \(x\), substitute it back into \(y = 2 - x\) to find the corresponding value of \(y\).

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Key Concepts

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

System of Linear Equations

A system of linear equations consists of two or more linear equations with the same set of variables. The goal is to find values for the variables that satisfy all equations simultaneously. In this problem, the system involves two equations with variables x and y.
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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. After finding one variable, substitute back to find the other.
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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, division, and simplifying expressions. Accurate manipulation is essential to correctly solve for variables in the system.
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Related Practice
Textbook Question

Write the system of equations associated with each augmented matrix . Do not solve.

[10020103001−2]\(\left\)[ \(\begin{matrix}\) 1 & 0 & 0 & 2 \\ 0 & 1 & 0 & 3 \\ 0 & 0 & 1 & -2 \(\end{matrix}\) \(\right\)]

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Textbook Question

Graph each inequality. x < 3 + 2y

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Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components.

y = x2 - 2x + 1

x - 3y = -1

Textbook Question

Find the cofactor of each element in the second row of each matrix.

[−201120421]\(\left\)[ \(\begin{matrix}\) -2 & 0 & 1 \\ 1 & 2 & 0 \\ 4 & 2 & 1 \(\end{matrix}\) \(\right\)]

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Textbook Question

Solve each problem using a system of equations. A company sells recordable CDs for \$0.80 each and play-only CDs for \$0.60 each. The company receives \$76.00 for an order of 100 CDs. However, the customer neglected to specify how many of each type to send. Determine the number of each type of CD that should be sent.

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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x^2 - x - 15)/(x(x + 1)(x - 1))