Math Problem Statement
3x + 7y = 16 4x - 3y = 9
Solution
We are given the system of linear equations:
We can solve this system by using the substitution method or elimination method. Let's use the elimination method to eliminate one variable.
Step 1: Multiply the equations to align the coefficients
We want to eliminate one of the variables by making the coefficients of either or equal in both equations. Let's eliminate .
To do that, we'll multiply Equation 1 by 3 and Equation 2 by 7 to make the coefficients of opposites of each other:
Step 2: Add the two equations to eliminate
Now, add Equation 3 and Equation 4:
Step 3: Solve for
Now, solve for :
Step 4: Substitute back into one of the original equations
Now that we know , substitute this value back into either Equation 1 or Equation 2. Let's substitute it into Equation 1:
Final Solution:
Thus, the solution to the system of equations is:
Would you like further details on how this solution was found? Let me know if you have any questions!
Here are some related questions to expand your understanding:
- What is the substitution method for solving a system of linear equations?
- How can you use matrix operations to solve a system of equations?
- What happens if the system of equations has no solution or infinitely many solutions?
- How can you graphically represent the solution of a system of linear equations?
- What is the concept of "linear independence" in a system of equations?
Tip: When using the elimination method, ensure that the coefficients of the variable you wish to eliminate are opposites. This can often simplify the process.
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Systems of Linear Equations
Elimination Method
Substitution Method
Formulas
Elimination method
Substitution method
Theorems
Linear systems solutions
Suitable Grade Level
Grades 8-10
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