To find : the solution to the given system of linear equations
Answer to Problem 35E
Letting
ordered triples of the form
Explanation of Solution
Given information : The system of equation is
Concept Involved:
Solution of a system of equation is the point which makes both the equation TRUE.
Graphically the solution to the system of equation is the point where the two lines meet.
Method of Elimination:
To use the method of elimination to solve a system of two linear equations in x and y, perform the following steps.
1. Obtain coefficients for x (or y) that differ only in sign by multiplying all
terms of one or both equations by suitably chosen constants.
2. Add the equations to eliminate one variable.
3. Solve the equation obtained in Step 2.
4. Back-substitute the value obtained in Step 3 into either of the original
equations and solve for the other variable.
5. Check that the solution satisfies each of the original equations.
The Number of Solutions of a Linear System
For a system of linear equations, exactly one of the following is true.
1. There is exactly one solution.
2. There are infinitely many solutions.
3. There is no solution.
Calculation:
Description | Steps | |
Label the given equations | ▶ 1st equation | |
▶ 2nd equation | ||
▶ 3rd equation | ||
In order to eliminate x , multiply -3 with the 2nd equation and add the result to the 1stequation | ||
Simplify the equation | ||
Label the new equation as 4th equation | ▶ 4th equation | |
In order to eliminatex , multiply -5 with the 2nd equation and add the result the 3rd equation | ||
Label the new equation as 5th equation | ▶ 5th equation | |
Multiply 18 with 4th equation and add the result with 5th equation | There are infinitely many solutions to the given system of equation | |
Let | ||
Substituting Distributing 2 in the left side of the equation Combine like terms Subtract 2 and | ||
Let a be any real number then the solution to the given system of equation is given by the coordinate |
Conclusion:
Letting
ordered triples of the form
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
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