One Solution, No Solution, Infinite Solutions

Front

What does it mean if an equation has infinitely many solutions?

Back

It means that there are an infinite number of values for the variable that satisfy the equation, often because the equation simplifies to a true statement (e.g., 0 = 0).

Front

What is a condition for an equation to have no solution?

Back

An equation has no solution when the two sides are contradictory, such as 2 = 3, meaning there is no value for the variable that can make the equation true.

Front

Solve: 3x + 15 = 3(x + 5)

Back

Infinitely Many Solutions

Front

What is the missing information that would make the statement FALSE for One solution? 4x + 5 = _ - 6

Back

4x

Front

Simplify: 3x - 7 = 3(x - 3) + 2. What type of solution does it have?

Back

Infinite solutions

Front

What is the missing information that would make the statement true for INFINITE solutions? _ + 10 = 5x + 10

Back

5x

Front

Solve: 6x + 9 – x = 3x + 9 + x

Back

One Solution

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form y = mx + b.

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

What is the general form of a linear equation?

Back

The general form is Ax + By = C, where A, B, and C are constants.