Skip to main content
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 15
Chapter 6, Problem 15

Find the values of the variables for which each statement is true, if possible.
[x+2y−6z−3w+5]=[−2803]\(\left\)[ \(\begin{matrix}\) x + 2 & y - 6 \\ z - 3 & w + 5 \(\end{matrix}\) \(\right\)] = \(\left\)[ \(\begin{matrix}\) -2 & 8 \\ 0 & 3 \(\end{matrix}\) \(\right\)]

Verified step by step guidance
1
First, carefully read the problem statement to identify the given equations or expressions involving the variables. Since the problem references Examples 1 and 2, review those examples to understand the type of equations or statements you are dealing with.
Next, write down the equations or inequalities explicitly. For example, if the problem involves solving for variables in an equation like \(a + b = c\), write it clearly to analyze the relationships.
Then, isolate one variable in terms of the others if possible. For instance, solve for \(a\) in terms of \(b\) and \(c\) by rearranging the equation: \(a = c - b\).
After that, substitute the expression from the previous step into any other equations or conditions given to reduce the number of variables and find possible values.
Finally, check the solutions obtained by substituting back into the original statements to verify if they satisfy all conditions. If no values satisfy the statements, conclude that no solution exists.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

Key Concepts

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

Solving Equations

Solving equations involves finding the values of variables that make the equation true. This process may include isolating the variable using inverse operations such as addition, subtraction, multiplication, division, or applying algebraic properties.
Recommended video:
5:02
Solving Logarithmic Equations

Checking for Extraneous Solutions

When solving equations, especially those involving variables on both sides or radicals, some solutions may not satisfy the original equation. It is important to substitute found values back into the original equation to verify their validity.
Recommended video:
05:21
Restrictions on Rational Equations

Understanding Variable Constraints

Variables may have restrictions based on the context or the equation type, such as denominators not being zero or expressions under square roots being non-negative. Recognizing these constraints helps determine the domain and valid solutions.
Recommended video:
Guided course
05:28
Equations with Two Variables
Related Practice
Textbook Question

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

x2 - y = 0

x + y = 2

545
views
Textbook Question

Solve each system by substitution.

-2x = 6y + 18

-29 = 5y - 3x

887
views
Textbook Question

Write the augmented matrix for each system and give its dimension. Do not solve. 4x - 2y + 3z - 4 = 0 3x + 5y + z - 7 = 0 5x - y + 4z - 7 = 0

1072
views
Textbook Question

Evaluate each determinant.

∣−7030∣\(\left\)| \(\begin{matrix}\) -7 & 0 \\ 3 & 0 \(\end{matrix}\) \(\right\)|

705
views
Textbook Question

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

[321102422−1−2315]\(\left\)[ \(\begin{matrix}\) 3 & 2 & 1 & 1 \\ 0 & 2 & 4 & 22 \\ -1 & -2 & 3 & 15 \(\end{matrix}\) \(\right\)]

868
views
Textbook Question

Graph each inequality. 4y - 3x ≤ 5

527
views