Table of contents

0. Review of Algebra4h 16m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 19m
10. Combinatorics & Probability1h 45m

7. Systems of Equations & Matrices

Determinants and Cramer's Rule

College Algebra

7. Systems of Equations & Matrices

Determinants and Cramer's Rule

2:08 minutes

Problem 5b

Textbook Question

What is the value of x if = 9?

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Key Concepts

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

Algebraic Equations

Algebraic equations are mathematical statements that assert the equality of two expressions. They often contain variables, constants, and operators. To solve for a variable, one must isolate it on one side of the equation, which involves performing inverse operations to both sides to maintain equality.

Isolating the Variable

Isolating the variable is a fundamental technique in solving equations. This process involves rearranging the equation so that the variable of interest is alone on one side. This is typically achieved by adding, subtracting, multiplying, or dividing both sides of the equation by the same number, ensuring that the equation remains balanced.

Substitution

Substitution is a method used in algebra to replace a variable with a known value or expression. In the context of solving equations, once the variable is isolated, substituting known values allows for the determination of the variable's value. This technique is essential for simplifying complex equations and finding solutions efficiently.