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 has one solution?

Back

If the lines intersect at exactly one point, the system has one unique solution.

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

Example of substitution: Solve the system: y = 2x + 3 and x + y = 10. What is the solution?

Back

(2, 7) - Substitute y from the first equation into the second.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

What does it mean if two equations are equivalent?

Back

They have the same solution set.