To Answer:
To solve the system of linear equations with three variables.
Answer to Problem 28E
Solution:
The solution of given system is
Explanation of Solution
1) Concept:
Step 1: Simplify and put all three equations in the form
Step 2: Use elimination method to eliminate any one of the variables. So that we get two equations with two unknowns.
Step 3: Solve the remaining system of equations just as solving a system of linear equations with two unknowns.
Step 4: Solve for the third variable.
Step 5: Check whether solved solutions satisfy the given system of equations by substituting the values obtained in the given system of linear equations.
2) Given:
Calculation:
From all the above three equations, we can observe that the coefficients of variables are in fractions.
To perform calculations easily, we can take L.C.M and make fraction as integers.
(I) Simplify all three equations
For simplifying (1) take L.C.M. By doing so, we get
By simplifying (2), we get
Simplifying (3), we get
Now the system of linear equations is
(II) We can choose to eliminate
On multiplying (4) by 4 and (5) by 3 and by subtracting the resultant, we can eliminate
Multiplying (3) by 4, we get
Multiplying (5) by 3, we get
Subtracting (7) from (8), we get
By multiplying (6) by 4 and subtracting from (4), we can eliminate
By multiplying (5) by 4, we get
Subtracting (5) from (10), we get
Now we have two equations with two unknowns, the two equations are
Solve for
Subtracting (9) and (11), we get
Substitute
III) Solve for third variable
Substitute
IV) Verify:
Substitute
Conclusion:
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Chapter 4 Solutions
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