2. Suppose you are given a linear system consisting of two linear equations in two variables of the form ax + by = e bx + dy = f Give examples of linear systems that have: (a) no solution, (b) exactly one solution, or (c) infinitely many solutions. Explain why these are the only possibilities. You may use some pictures to help explain your reasons.
2. Suppose you are given a linear system consisting of two linear equations in two variables of the form ax + by = e bx + dy = f Give examples of linear systems that have: (a) no solution, (b) exactly one solution, or (c) infinitely many solutions. Explain why these are the only possibilities. You may use some pictures to help explain your reasons.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. Suppose you are given a linear system consisting of two linear equations in two variables of the form
ax + by = e
bx + dy = f
Give examples of linear systems that have:
(a) no solution,
(b) exactly one solution, or
(c) infinitely many solutions.
Explain why these are the only possibilities. You may use some pictures to help explain your reasons.
Expert Solution
Step 1
A system of linear equations is defined as one that contains two or more equation linear equations. Let us consider two equation is,
A system of the equation has no solution if .
A system of the equation exactly one solution if .
A system of the equation infinitely solution if .
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