Solving Systems with 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 make all equations in the system true.

Front

What is substitution 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

Isolate one variable in one of the equations.

Front

If you have the equations y = 2x + 3 and y = -x + 1, how do you solve them using substitution?

Back

Set 2x + 3 = -x + 1 and solve for x.

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

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

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the values back into the original equations to see if they hold true.

Front

What is the solution to the system of equations: 2x + 3y = 12 and x - y = 2?

Back

(3, 2) is the solution.

Front

What is the graphical representation of a system of equations?

Back

The intersection point(s) of the lines representing the equations on a graph.