One Solution, No Solution, Infinite Solutions

Front

What are the three types of solutions for linear equations?

Back

One solution, no solution, infinite solutions.

Front

What does it mean if an equation has no solution?

Back

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

Front

What is an example of an equation with infinite solutions?

Back

An example is 3(x-2) + 1 = 3x - 5, which simplifies to a true statement.

Front

How can you determine if an equation has one solution?

Back

If you can isolate the variable and find a specific value that satisfies the equation, it has one solution.

Front

What is the significance of the coefficients in an equation?

Back

Coefficients determine the slope and position of the line represented by the equation.

Front

What does it mean for an equation to have one solution?

Back

It means there is exactly one value for the variable that satisfies the equation.

Front

How do you identify an equation with no solution?

Back

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

Front

What is the first step in solving a linear equation?

Back

The first step is to simplify both sides of the equation as much as possible.

Front

What is the role of constants in linear equations?

Back

Constants are fixed values that can shift the position of the line on the graph.

Front

What is the difference between dependent and independent equations?

Back

Dependent equations have infinite solutions, while independent equations have exactly one solution.