Systems of Equations

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 for a system of equations to be consistent?

Back

A consistent system has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions.

Front

What does it mean for a system of equations to be dependent?

Back

A dependent system has infinitely many solutions, as the equations represent the same line.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

How do you graph a system of equations?

Back

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

Front

What is the solution to the system of equations 2x - 3y = 6 and 7x - 3y = -9?

Back

(-3,-4)

Front

What is the solution to the system of equations 3x - 2y = -8 and 5x + 2y = -8?

Back

(-2,1)

Front

What is the solution to the system of equations x - 2y = 4 and 3x + 2y = 4?

Back

(2,-1)