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 infinite solutions?

Back

It means that the equation is true for all values of the variable, often resulting from identical expressions on both sides.

Front

What does it mean if an equation has no solutions?

Back

It means that there is no value of the variable that can satisfy the equation, often resulting from contradictory statements.

Front

How can you determine if an equation has one solution?

Back

If simplifying the equation leads to a single value for the variable, it has one solution.

Front

What is the first step in solving a linear equation?

Back

Isolate the variable on one side of the equation.

Front

What is the significance of simplifying both sides of an equation?

Back

It helps to identify the type of solution the equation has (one, none, or infinite).

Front

What is an example of an equation with infinite solutions?

Back

3x - 7 = 3(x - 3) + 2 simplifies to an identity.

Front

What is an example of an equation with no solutions?

Back

2x + 1 = 2x - 1 simplifies to a contradiction.

Front

What does it mean for two equations to be equivalent?

Back

They have the same solution set.

Front

How do you check if your solution to an equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.