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 no solution?

Back

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

Front

How do you solve a system of equations by graphing?

Back

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

Front

What is the substitution method for solving systems of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

Add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the solution to the system of equations 2x + 3y = 6 and x - y = 1?

Back

(3, 0) is the solution.

Front

What is the graphical representation of the solution to a system of equations?

Back

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

Front

What does it mean if two equations are dependent?

Back

It means they represent the same line and have infinitely many solutions.

Front

What does it mean if two equations are independent?

Back

It means they represent different lines that intersect at exactly one point.