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To find : the solution to the given system of linear equations
![Check Mark](/static/check-mark.png)
Answer to Problem 36E
The solution to the given system of equation is
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 y, add 1st and 2nd equation | ||
In order to solve for x Divide by -1 on both sides of the equation Simplifying fraction both sides | ||
In order to eliminate the same y variable, multiply 2 with the 3rd equation and add the result to the 2ndequation | ||
Label the new equation as 4th equation | ▶ 4th equation | |
Substitute 3 for x in the 4th equation and solve for z Add 3 on both sides Divide -4 on both sides Simplify fraction on both sides of the equation | ||
Substitute |
Calculation (Continued):
Description | Steps |
Checking the solution | |
Checking the solution | |
Checking the solution |
Conclusion:
The solution to the given system of equation is
Chapter 7 Solutions
Precalculus with Limits
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