Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations that have the same variables.

Front

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

Back

(1, 3)

Front

Find the solution to the system: y = x - 6 and y = -3x + 2

Back

(2, -4)

Front

What does the graph of a system of equations with no solution look like?

Back

Parallel lines.

Front

What is the solution type when a system of equations has infinitely many solutions?

Back

Infinitely Many Solutions.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

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

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

Back

The system has one unique solution.

Front

What is the graphical representation of a system of equations with exactly one solution?

Back

Two intersecting lines.

Front

What does it mean if two equations are dependent?

Back

They represent the same line and have infinitely many solutions.