What is a system of equations?
Systems of Equations

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•
Mathematics
•
8th - 11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.
2.
FLASHCARD QUESTION
Front
What does it mean if a system of equations has a unique solution?
Back
A unique solution means that there is exactly one set of values for the variables that satisfies all equations in the system.
3.
FLASHCARD QUESTION
Front
What does it mean if a system of equations has no solution?
Back
No solution means that there is no set of values for the variables that can satisfy all equations in the system, often due to parallel lines.
4.
FLASHCARD QUESTION
Front
What does it mean if a system of equations has infinitely many solutions?
Back
Infinitely many solutions occur when the equations represent the same line, meaning any point on the line is a solution.
5.
FLASHCARD QUESTION
Front
How can you determine if a system of equations has a unique solution, no solution, or infinitely many solutions?
Back
You can determine this by graphing the equations or using methods like substitution or elimination to analyze the relationships between the equations.
6.
FLASHCARD QUESTION
Front
What is the substitution method in solving systems of equations?
Back
The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.
7.
FLASHCARD QUESTION
Front
What is the elimination method in solving systems of equations?
Back
The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.
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