Equations with one solution, no solutions, or infinite

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•
Mathematics
•
7th - 9th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is an equation with one solution?
Back
An equation with one solution is a linear equation that can be solved to yield a single unique value for the variable. For example, the equation 2x + 3 = 7 has one solution: x = 2.
2.
FLASHCARD QUESTION
Front
What does it mean for an equation to have no solutions?
Back
An equation has no solutions when there is no value for the variable that can satisfy the equation. This often occurs when the equation simplifies to a false statement, such as 0 = 5.
3.
FLASHCARD QUESTION
Front
What is an equation with infinitely many solutions?
Back
An equation with infinitely many solutions is one where any value of the variable satisfies the equation. This typically happens when the equation simplifies to a true statement, such as 0 = 0.
4.
FLASHCARD QUESTION
Front
How do you determine if an equation has no solutions?
Back
To determine if an equation has no solutions, simplify the equation and check if it leads to a contradiction, such as a false statement (e.g., 5 = 0).
5.
FLASHCARD QUESTION
Front
What is the first step in solving a linear equation?
Back
The first step in solving a linear equation is to isolate the variable on one side of the equation, often by using inverse operations.
6.
FLASHCARD QUESTION
Front
What is the significance of coefficients in linear equations?
Back
Coefficients are the numerical factors that multiply the variables in an equation. They affect the slope and position of the line represented by the equation.
7.
FLASHCARD QUESTION
Front
What is the process of combining like terms in an equation?
Back
Combining like terms involves adding or subtracting terms that have the same variable raised to the same power to simplify the equation.
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