Math Problem Statement
Solution
The given system of equations is:
To solve this system, you can either use substitution or elimination. I will demonstrate the elimination method since the coefficients of and are already opposites.
Step 1: Add the two equations
The terms and cancel out, as do and . Therefore, we get:
Step 2: Interpret the result
The equation is true for all values of and , meaning the system has infinitely many solutions. The two equations represent the same line, and any point on that line is a solution.
So, this system has infinitely many solutions.
Would you like further clarification on this? Here are some related questions to explore:
- How can you graph the solution to this system?
- How do you solve systems of equations using substitution?
- How do you interpret systems with no solutions?
- What does it mean geometrically when two equations represent the same line?
- What is the difference between dependent and independent systems?
Tip: Always check the result of adding or subtracting the equations in elimination method to see if you get a true or false statement. If it's true, the system has infinite solutions; if false, it has no solutions.
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Math Problem Analysis
Mathematical Concepts
Systems of Linear Equations
Elimination Method
Formulas
Elimination method: Adding or subtracting equations to eliminate variables
Theorems
Systems with infinitely many solutions (dependent systems)
Zero equals zero (indicating infinite solutions)
Suitable Grade Level
Grades 7-10
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