To find: the solution of the system and the conditions should be placed on the constants in the system to be certain that the system has a unique solution.
Answer to Problem 40WE
The system has a solution
Explanation of Solution
Given information:
The system of the equation is
Calculation:
Assume that the system
The values of a , b , c , and d are computed as follows,
Find the linear combination that eliminates the variable y .
Since the least common multiple of the y’s coefficients b and a is ab , multiply first equation by a and multiply second equation by b .
Add these two equations to simplify,
Simplify further to find the values of x ,
Here, the denominator of
That is,
Thus, the value of
Substitute
Simplify further to find the value of y ,
Divide on both sides by a ,
Thus, the value of
Therefore, the system has a solution
Chapter 3 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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