No Solution, One Solution, Infinite Solutions

Front

What does it mean when an equation has infinite solutions?

Back

An equation has infinite solutions when both sides of the equation are identical, meaning any value for the variable will satisfy the equation.

Front

What is an example of an equation with infinite solutions?

Back

An example is -10y - 6 = -10y - 6, where both sides are the same.

Front

What does it mean when an equation has no solution?

Back

An equation has no solution when it leads to a contradiction, meaning there is no value for the variable that can satisfy the equation.

Front

What is an example of an equation with no solution?

Back

An example is 2(m + 3) = 2m + 12, which simplifies to a false statement.

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 is 6(m + 3) = 5(m - 2), which simplifies to a single value for m.

Front

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

Back

You can determine this by simplifying the equation and analyzing the resulting statements. If both sides are identical, it has infinite solutions; if it leads to a contradiction, it has no solution; if it simplifies to a single value, it has one solution.

Front

What is the significance of the coefficients in determining the number of solutions?

Back

The coefficients of the variables in an equation help determine the relationship between the variables. If they are proportional in a way that leads to a contradiction, there is no solution; if they are identical, there are infinite solutions.

Front

What is the first step in solving an equation to find its solutions?

Back

The first step is to simplify both sides of the equation as much as possible, combining like terms and isolating the variable.

Front

What is a contradiction in the context of equations?

Back

A contradiction occurs when an equation simplifies to a statement that is always false, such as 0 = 5.