Math Problem Statement
Solution
The problem involves solving a system of linear equations:
Steps to Solve the System:
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Write the equations in standard form: Equation 1:
Equation 2:
Equation 3: . -
Eliminate by adding or subtracting equations:
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From Equation 2 and Equation 3:
Add Equation 2 () and Equation 3 ():
Simplify: :
-
From Equation 1 and Equation 3:
Subtract Equation 3 from Equation 1:
Simplify:
:
-
-
Solve the reduced system ( and ):
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Multiply Equation A by 3 and Equation B by 2 to eliminate :
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Add the two equations:
Simplify:
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Substitute into Equation A:
Simplify:
-
-
Find using any original equation:
Substitute and into Equation 2 ():
Simplify:
Final Solution:
Would you like further clarification or step-by-step verification?
5 Follow-Up Questions:
- How can systems of equations be solved using matrix methods?
- What are the benefits of elimination over substitution in solving systems?
- Can graphing always determine solutions for linear systems? Why or why not?
- How would the solution change if one equation were inconsistent?
- How
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Systems of Equations
Formulas
Substitution Method
Elimination Method
Theorems
Properties of Linear Systems
Solution Uniqueness for Linear Systems
Suitable Grade Level
Grades 9-12
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