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 a linear equation has infinite solutions?

Back

It means that the two sides of the equation are equivalent for all values of the variable.

Front

How can you determine if a linear equation has no solution?

Back

If the equation simplifies to a false statement, such as 0 = 5.

Front

What is the first step in solving a linear equation?

Back

Isolate the variable by performing inverse operations.

Front

What does it mean if two equations are equivalent?

Back

They represent the same line on a graph and have the same solution set.

Front

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

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

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

Back

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

Front

What is the general form of a linear equation?

Back

Ax + By = C, where A, B, and C are constants.

Front

What is the difference between a consistent and inconsistent system of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.