Math Problem Statement
x+2y-3z= -4 2x+y-3z= 4 solve by elimination method
Solution
To solve the system of equations by the elimination method, let’s start with the system:
Step 1: Eliminate by subtracting Equation (1) from Equation (2).
To eliminate , notice that both equations contain with the same coefficient. By subtracting Equation (1) from Equation (2), we can remove from the equations:
Simplify each side:
This simplifies to:
Step 2: Solve Equation (3) for in terms of :
From Equation (3), we have:
Step 3: Substitute into one of the original equations.
Let’s substitute into Equation (1):
Simplify this:
Subtract 8 from both sides:
Divide through by 3:
Step 4: Solve Equation (4) for in terms of :
From Equation (4), we have:
Step 5: Substitute back into :
Substitute into :
Simplify:
Conclusion:
The solution to this system in terms of is:
Therefore, the solution set is all points that satisfy:
If you have a specific value for , you can substitute it to find the corresponding values of and .
Would you like more details or have questions on this method? Here are five follow-up questions to consider:
- What happens if we use a different elimination strategy?
- How can we verify the solution by substitution?
- What is the geometric interpretation of this solution set?
- Can we express the solution in a parametric form?
- How does elimination differ from substitution for this system?
Tip: Always double-check your solution by plugging it back into the original equations to ensure accuracy.
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Linear Equations
Elimination Method
Formulas
Elimination method for solving systems of linear equations
Linear combination of equations
Theorems
Properties of equality in linear systems
Suitable Grade Level
Grades 10-12
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