Math Problem Statement
Solve the following system of equations. Write your answer as a point (π₯, π¦).
π₯ + 3π¦ = 3 3π₯ + π¦ = 17
Solution
To solve the system of equations:
Step 1: Solve one equation for one variable
From the first equation, solve for in terms of :
Step 2: Substitute into the second equation
Substitute into the second equation: Simplify:
Step 3: Solve for
Substitute back into :
Final Answer:
The solution to the system is:
Would you like a detailed explanation or have any questions?
Related Questions:
- What are some alternative methods to solve systems of equations (e.g., elimination)?
- How can you verify that a solution to a system of equations is correct?
- Can this system of equations be solved graphically? How?
- What would the solution be if one of the equations were modified?
- How does solving systems of equations differ for non-linear systems?
Tip: Always double-check your solution by substituting the values back into the original equations.
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Linear Equations
Substitution Method
Formulas
Substitution Method: Replace one variable with its equivalent from another equation
Simplification of linear equations
Theorems
Properties of Equality
Suitable Grade Level
Grades 8-10
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