Infinite/No Solution/One Solution

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that will satisfy the equation.

Front

What is the definition of infinite solutions?

Back

An equation has infinite solutions if any value of the variable will satisfy the equation.

Front

What is the definition of one solution?

Back

Only this ONE solution will make the equation true.

Front

How can you determine if an equation has no solution?

Back

If simplifying the equation leads to a contradiction, such as 0 = 5, it has no solution.

Front

What is an example of an equation with infinite solutions?

Back

An example is 2(x + 1) = 2x + 2.

Front

What is an example of an equation with one solution?

Back

An example is 3x + 2 = 11, which has the solution x = 3.

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set.

Front

How do you solve for a variable in an equation?

Back

Isolate the variable on one side of the equation using inverse operations.

Front

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

Back

The slope indicates the rate of change of the dependent variable with respect to the independent variable.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.