
a.
To construct: The system of linear equations with three variables such that it has no solution.
a.

Answer to Problem 82AYU
The system of linear equations with three variables such that it has no solution is,
Explanation of Solution
Given information:
The system of linear equations with three variables such that it has no solution.
Consider the system of linear equations with three variables.
Recall that parallel lines have no solution because they never intersect.
Two lines are said to be parallel if the ratio of the coefficients of the lines are equal.
Suppose take an equation of line with three variables as,
Now, multiply the coefficient of equation by three to obtain the second equation
Take a random third equation
Now, system of equations so formed is,
Since, first two equations are parallel because the coefficients have same ratio so the system has no solution. Because two lines out of three are parallel.
b.
To construct: The system of linear equations with three variables such that it has exactly one solution.
b.

Answer to Problem 82AYU
The system of linear equations with three variables such that it has exactly one solution is,
Explanation of Solution
Given information:
The system of linear equations with three variables such that it has exactly one solution.
Consider the system of linear equations with three variables.
Recall that intersecting lines can either intersect at one or two points.
Two lines are said to be intersecting if the ratio of the coefficients of the lines are not equal
Suppose take an equation of line with three variables as,
Now, the second equation
Take a random third equation
Now, system of equations so formed is,
Since, the coefficients of all the three lines are in same ratio so the system has exactly one solution.
c.
To construct: The system of linear equations with three variables such that it has infinitely many solutions.
c.

Answer to Problem 82AYU
The system of linear equations with three variables such that it has infinitely many solutions is,
Explanation of Solution
Given information:
The system of linear equations with three variables such that it has infinitely many solutions.
Consider the system of linear equations with three variables.
Recall that coincident lines have infinitely many solutions.
Two lines are said to be coincident if the ratio of the coefficients of the lines are equal.
Suppose take an equation of line with three variables as,
Now, the second equation
Take a random third equation
Now, system of equations so formed is,
Since, the coefficients of all the two lines are in same ratio so the system has infinitely many solutions.
Chapter 11 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
College Algebra (7th Edition)
University Calculus: Early Transcendentals (4th Edition)
A First Course in Probability (10th Edition)
Elementary Statistics
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