Solving Systems with 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 a system of equations?

Back

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

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 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 do you determine if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other.

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 is the solution to the system of equations: 2x + 3y = 6 and x - y = 2?

Back

(3, 0) is the solution.

Front

What does it mean for two equations to be dependent?

Back

They represent the same line and have infinitely many solutions.