1 solution, no solution, infinite solutions

Front

What does it mean when an equation has one solution?

Back

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

Front

What does it mean when an equation has no solution?

Back

An equation has no solution when there is no value of the variable that can satisfy the equation, often resulting in a contradiction.

Front

What does it mean when an equation has infinite solutions?

Back

An equation has infinite solutions when any value of the variable satisfies the equation, indicating that the two sides of the equation are equivalent.

Front

How do you determine if an equation has no solution?

Back

You can determine if an equation has no solution by simplifying it to a contradiction, such as 0 = 5.

Front

What is the first step in solving a linear equation?

Back

The first step in solving a linear equation is to isolate the variable on one side of the equation.

Front

What is the solution to the equation 3y - 8 = 7y?

Back

The solution is y = -4.

Front

What is the solution to the equation 2x + 1 = 2x - 1?

Back

The equation has no solution.

Front

What is the solution to the equation 3y + 6 + 4y - 7 = -8?

Back

The solution is y = -1.

Front

What is the solution to the equation 8m + 12 = 2(4m + 6)?

Back

The equation has infinite solutions.

Front

What is a contradiction in the context of equations?

Back

A contradiction is a statement that cannot be true, such as 0 = 5, indicating that the equation has no solution.