Systems of Equations --- Substitution

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 for a variable in an equation?

Back

To isolate the variable on one side of the equation to find its value.

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 solving a system of equations using substitution?

Back

Solve for y or x in one equation.

Front

What do you do after substituting a variable in a system of equations?

Back

Solve the resulting equation for the remaining variable.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect.

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

Front

How do you check your solution for a system of equations?

Back

Substitute the values of the variables back into the original equations to verify they hold true.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations on a coordinate plane.