System of Equations - graphing and substitution 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 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 infinite 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

You graph both equations on the same coordinate plane and identify the point(s) where they intersect.

Front

What is the substitution method in solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

Front

What is the first step in the substitution method?

Back

Get either variable by itself.

Front

Solve for x and y: y = 2x + 1 and y = 4x - 1.

Back

(1, 3)

Front

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

Back

(3, 0)

Front

If two lines intersect at a point, what does that indicate about the system of equations?

Back

It indicates that there is a unique solution to the system.

Front

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

Back

The two equations are represented by the same line.