How many solutions does this linear equation have?

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What does it mean if a linear equation has infinite solutions?

Back

It means that the equation is true for all values of the variable, indicating that the two sides of the equation are equivalent.

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What does it mean if a linear equation has one solution?

Back

It means that there is exactly one value of the variable that makes the equation true.

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What does it mean if a linear equation has no solution?

Back

It means that there is no value of the variable that can satisfy the equation, indicating a contradiction.

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Example of an equation with infinite solutions: 5x + 3 = 5x + 3. What is the solution?

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Infinite solutions.

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Example of an equation with one solution: x = -9. What is the solution?

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One solution.

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Example of an equation with no solution: 5 = 2. What is the solution?

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No solution.

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What is the general form of a linear equation?

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A linear equation can be expressed in the form ax + b = c, where a, b, and c are constants.

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How can you determine if a linear equation has no solution?

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If simplifying the equation leads to a false statement, such as 5 = 2, it has no solution.

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How can you determine if a linear equation has infinite solutions?

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If simplifying the equation leads to a true statement, such as 0 = 0, it has infinite solutions.

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

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The coefficients determine the slope and position of the line represented by the equation.