(a)
To prefer: substitution method or the elimination method to solve a system of two linear equations in two variables.
(a)
Answer to Problem 2RCC
The substitution method ispreferred.
Explanation of Solution
In a system two linear equations in two variables, the substitution method has the advantage of being direct and straightforward.
However, it is possible that solving one equation for one variable yields a cumbersome expression.
Thus,
One may perform a number of operations after substituting only to find that the two equations are in fact the same, or that there are no solutions.
In comparison, the elimination method, while not a direct approach, has the advantage of letting one see when the system will have infinitely many solutions or no solutions before performing several operations.
(b)
To find:the number of possible solutions and draw the diagrams of possibilities.
(b)
Answer to Problem 2RCC
There are three possible solutions.
Explanation of Solution
Calculation:
A system of two linear equations in two variables has three possible scenarios: one unique solution, infinitely many solutions, or no solution.
In the case of a unique solution, the graphs of the system intersect at exactly one point.
In the case of infinitely many solutions, the graphs of the system intersect everywhere. The two equations have the same graph.
In the case of no solutions, the graphs do not intersect at all.
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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