Number of Solutions

Number of Solutions

Assessment

Flashcard

Mathematics

8th Grade

Hard

Created by

Wayground Content

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one, and it can be written in the form ax + b = c, where a, b, and c are constants.

2.

FLASHCARD QUESTION

Front

How can you determine the number of solutions for a linear equation?

Back

The number of solutions for a linear equation can be determined by analyzing the relationship between the coefficients of the variables. If the equation simplifies to a true statement (e.g., 0 = 0), it has infinite solutions. If it simplifies to a false statement (e.g., 0 = 5), it has no solution. If it results in a unique value for the variable, it has one solution.

3.

FLASHCARD QUESTION

Front

What does it mean if an equation has one solution?

Back

An equation has one solution if there is exactly one value of the variable that satisfies the equation.

4.

FLASHCARD QUESTION

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there is no value of the variable that can satisfy the equation, often resulting in a contradiction.

5.

FLASHCARD QUESTION

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions if any value of the variable satisfies the equation, indicating that the two sides of the equation are equivalent for all values of the variable.

6.

FLASHCARD QUESTION

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation determine the slope and position of the line represented by the equation on a graph.

7.

FLASHCARD QUESTION

Front

How do you solve the equation 3x + 1 = 8 + 2x?

Back

To solve 3x + 1 = 8 + 2x, subtract 2x from both sides to get x + 1 = 8. Then, subtract 1 from both sides to find x = 7. This equation has one solution.

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