Solve systems of equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations by substitution?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the graphical representation of a system of equations?

Back

The solution is the point(s) where the graphs of the equations intersect.

Front

What does it indicate if two equations represent parallel lines?

Back

The system has no solution because the lines never intersect.

Front

What does it indicate if two equations represent the same line?

Back

The system has infinitely many solutions because every point on the line is a solution.

Front

How can you determine if a system of equations has no solution?

Back

If the equations are inconsistent, meaning they represent parallel lines.

Front

What is the solution to the system of equations y = 2x and y = 3x + 1?

Back

The solution is (-1, -2).

Front

What is an example of a statement that results in no solution when solving a system of equations?

Back

If the equations simplify to a false statement, such as 2 = 3.

Front

What is an example of a statement that results in infinite solutions?

Back

If the equations simplify to a true statement, such as 2 = 2.

Front

What is the substitution method used for?

Back

To solve systems of equations when one equation can be easily solved for one variable.