Systems of Equations REVIEW

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 are the three main methods to solve systems of equations?

Back

1. Graphing 2. Substitution 3. Elimination

Front

What is the substitution method?

Back

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

Front

What is the elimination method?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you graph a system of equations?

Back

Plot each equation on the same coordinate plane and identify the point(s) where they intersect.

Front

What is the first step in solving a system using substitution?

Back

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

Front

What is the first step in solving a system using elimination?

Back

Align the equations and manipulate them (if necessary) to have the same coefficients for one variable.

Front

Solve the system: y = 2x + 3 and x + y = 10.

Back

(2, 6)