Solving 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 have a unique solution?

Back

It means that the lines represented by the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

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

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that the lines represented by the equations coincide, or are the same line.

Front

How can you determine if two lines are parallel?

Back

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

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

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

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves graphing both equations on the same coordinate plane and identifying the point(s) of intersection.

Front

Solve: 2x + 3y = 6 and x - y = 1. What are x and y?

Back

x = 3, y = 0.

Front

Solve: 3x - 2y = 4 and 6x - 4y = 8. What are x and y?

Back

Infinitely many solutions.