One Solution, No Solution, Infinite Solutions

Front

What are the three types of solutions for a system of equations?

Back

One solution, no solution, infinite solutions.

Front

What does it mean if an equation has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean if an equation has infinite solutions?

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

How can you determine if two equations have one solution?

Back

If the lines represented by the equations intersect at exactly one point.

Front

What is the significance of the coefficients in determining the number of solutions?

Back

The coefficients of the variables determine the slope and position of the lines; if they are the same, the lines are parallel (no solution) or the same line (infinite solutions).

Front

What is the first step in solving a linear equation?

Back

Isolate the variable on one side of the equation.

Front

What does it mean to simplify an equation?

Back

To combine like terms and reduce the equation to its simplest form.

Front

What is an example of an equation with infinite solutions?

Back

3x + 15 = 3(x + 5) simplifies to 0 = 0.

Front

What is an example of an equation with no solution?

Back

2x + 3 = 2x + 5 simplifies to 3 = 5.

Front

What is the role of the equal sign in an equation?

Back

It indicates that the expressions on both sides of the equation are equivalent.