Equations with one solution, no solutions, or infinite solution

Front

What is an equation with infinite solutions?

Back

An equation that is true for all values of the variable, meaning both sides of the equation are identical after simplification.

Front

Example of an equation with infinite solutions: 8m + 12 = 2(4m + 6)

Back

Infinite Solutions

Front

What is an equation with no solution?

Back

An equation that has no values of the variable that can satisfy it, meaning both sides of the equation are never equal.

Front

Example of an equation with no solution: 9y + 8 = 9y - 8

Back

No Solution

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form ax + b = c.

Front

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

Back

By simplifying the equation and checking if it leads to a true statement (infinite solutions), a false statement (no solution), or a specific value (one solution).

Front

Example of an equation with one solution: 6(m + 3) = 5(m - 2)

Back

x = -28

Front

What does it mean if two equations are equivalent?

Back

They have the same solution set, meaning they represent the same line when graphed.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients determine the slope and position of the line on a graph.

Front

What is the first step in solving a linear equation?

Back

Isolate the variable by performing inverse operations on both sides of the equation.