Math Problem Statement
- (a)
Solution
To solve part (a) of the system of equations, let's rewrite the equations for clarity:
Step 1: Eliminate from two pairs of equations.
We subtract the first equation from the second and third equations:
From equation (2) - equation (1): 3x + y = -1 \tag{4}
From equation (3) - equation (1): 8x + 2y = 6 \tag{5}
Step 2: Solve the system of two equations in two variables ( and ).
Equations (4) and (5) are:
Multiply equation (4) by 2 to align coefficients of : 6x + 2y = -2 \tag{6}
Subtract equation (6) from equation (5):
Substitute into equation (4):
Step 3: Solve for .
Substitute and into the first equation:
Final Solution:
Would you like a detailed explanation of any step or help with part (b)?
Related Questions:
- How would this approach change for systems with more variables?
- What are alternative methods for solving systems of equations (e.g., matrix methods)?
- How can graphing help visualize solutions to such systems?
- What is the significance of consistency in a system of equations?
- How does elimination compare to substitution in terms of solving efficiency?
Tip:
Always verify solutions by substituting back into the original equations to ensure accuracy!
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Systems of Linear Equations
Elimination Method
Formulas
Equations of the form ax + by + cz = d
Theorems
Elimination Method
Consistency in Systems of Equations
Suitable Grade Level
Grades 9-12
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