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 is the graphical representation of a system of equations?

Back

The solution is the point(s) where the graphs of the equations intersect.

Front

What is the substitution method 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 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 determine if two lines are parallel in a system of equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the solution to the system: 5x - 4y = -16 and x + 2y = -6?

Back

(-4, -1)

Front

What is the solution to the system: 5x + 3y = 6 and x - 3y = 12?

Back

(3, -3)

Front

What is the solution to the system: x - 2y = -2 and 3x - 2y = 6?

Back

(4, 3)