To find : the solution to the given system of linear equations
Answer to Problem 25E
The solutions to the given system of equation are
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 Substitution:
1. Solve one of the equations for one variable in terms of the other.
2. Substitute the expression found in Step 1 into the other equation to obtain an equation in one variable.
3. Solve the equation obtained in Step 2.
4. Back-substitute the value obtained in Step 3 into the expression obtained in Step 1 to find the value of the other variable.
5. Check that the solution satisfies each of the original equations.
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.
Calculation:
Description | Steps | |
Label the given equations | ▶ 1st equation | |
▶ 2nd equation | ||
▶ 3rd equation | ||
In order to eliminate z divide the 2nd equation by 2 and add the result with the first equation | ||
Label the new equation as 4th equation | ▶ 4th equation | |
In order to eliminate variable z we can add 1st and 3rd equation | ||
Label the new equation as 5th equation | ▶ 5th equation | |
In order to eliminate x multiply -1 with the 4th equation and add the result with the 5th equation | ||
Solve the resulting equation | ||
Substituting 1/2 for y in the 4th equation and solve for x Simplifying fraction in left side of the equation Subtract 1 on both sides of the equation Dividing by 3 on both sides Simplify fraction on both sides | ||
Substituting 1 for x, |
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
EBK PRECALCULUS W/LIMITS
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