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
Two Variable Systems of Linear Equations
3:11 minutes
Problem 1`
Textbook Question
Textbook QuestionAnswer each of the following. When appropriate, fill in the blank to correctly complete the sentence. The following nonlinear system has two solutions, one of which is (3,____). x + y = 7 x^2 + y^2 = 25
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
3mPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Linear Equations
Linear equations represent relationships between variables that can be graphed as straight lines. In the given question, the equation x + y = 7 is a linear equation, indicating that for any value of x, there is a corresponding value of y that satisfies this equation. Understanding how to manipulate and solve linear equations is essential for finding the values of variables in a system.
Recommended video:
06:00
Categorizing Linear Equations
Nonlinear Equations
Nonlinear equations involve variables raised to a power greater than one or involve products of variables, resulting in curves rather than straight lines when graphed. The equation x^2 + y^2 = 25 is a nonlinear equation representing a circle with a radius of 5 centered at the origin. Recognizing the nature of nonlinear equations is crucial for solving systems that include both linear and nonlinear components.
Recommended video:
Guided course
3:21
Nonlinear Inequalities
Systems of Equations
A system of equations consists of two or more equations that share common variables. The goal is to find the values of these variables that satisfy all equations simultaneously. In this case, the system includes one linear and one nonlinear equation, and solving it requires finding points that lie on both graphs, which can yield multiple solutions, as indicated in the question.
Recommended video:
Guided course
4:27
Introduction to Systems of Linear Equations