Math Problem Statement
a+b+c=0 4a+2b+c=-4 9a+3b+c=-18
Solution
We have a system of three linear equations:
Step 1: Eliminate
To eliminate , we will subtract the first equation from the second and the second from the third.
Subtract equation (1) from equation (2):
This is equation (4).
Subtract equation (2) from equation (3):
This is equation (5).
Step 2: Solve the system of equations with two variables
Now we have two equations:
Subtract equation (1) from equation (2):
Step 3: Substitute into one of the equations
Substitute into equation :
Step 4: Solve for
Now substitute and into the first equation :
Final Solution:
Let me know if you want any details or have questions.
Here are 5 related questions:
- How can you verify if the solution is correct by substituting it back into the original equations?
- What is the general method for solving systems of equations using elimination?
- How would you solve this system using matrix methods such as Gaussian elimination?
- Can this system be solved using substitution instead of elimination?
- How would this problem change if the equations were non-linear?
Tip: To quickly check your solution, always substitute the values back into the original equations to confirm they hold true.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Systems of Equations
Formulas
Equation Elimination Method
Substitution Method
Theorems
Elimination of Variables
Solving Systems of Linear Equations
Suitable Grade Level
Grades 9-12
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