No Solution, One Solution, Infinite Solutions

Front

What does it mean when an equation has no solution?

Back

An equation has no solution when there are no values for the variable that can satisfy the equation. This often occurs when simplifying leads to a contradiction, such as 0 = 5.

Front

What is an example of an equation with no solution?

Back

An example of an equation with no solution is 9y + 8 = 9y - 8, which simplifies to 8 = -8, a contradiction.

Front

What does it mean when an equation has infinite solutions?

Back

An equation has infinite solutions when any value for the variable satisfies the equation. This typically occurs when both sides of the equation are equivalent after simplification.

Front

What is an example of an equation with infinite solutions?

Back

An example of an equation with infinite solutions is -10y - 6 = -10y - 6, which is true for all values of y.

Front

What does it mean when an equation has one solution?

Back

An equation has one solution when there is exactly one value for the variable that satisfies the equation.

Front

What is an example of an equation with one solution?

Back

An example of an equation with one solution is 5x - 8 = 4(x - 2), which simplifies to x = 2.

Front

How can you determine if an equation has no solution, one solution, or infinite solutions?

Back

To determine the type of solution, simplify the equation and analyze the resulting statements. Look for contradictions (no solution), equivalent expressions (infinite solutions), or a single value (one solution).

Front

What is the significance of the coefficients in an equation?

Back

Coefficients determine the relationship between variables in an equation. They affect the slope and position of the line represented by the equation in a graph.

Front

What is the role of constants in equations?

Back

Constants are fixed values in equations that can shift the graph of the equation up or down, affecting the y-intercept.

Front

What is the process of solving a linear equation?

Back

The process of solving a linear equation involves isolating the variable on one side of the equation through algebraic operations such as addition, subtraction, multiplication, and division.