System of Equations (Substitution)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the first step in the substitution method?

Back

Find the equation that is solved for the single variable.

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines representing the equations coincide, meaning they are the same line.

Front

How can you identify a system of equations with no solution?

Back

If you simplify the equations and end up with a false statement, like 4 = 7.

Front

What is an example of a system of equations with one solution?

Back

x + y = 0 and x - y = 2.

Front

What is an example of a system of equations with no solution?

Back

x + y = 1 and x + y = 3.