Systems of Equations

Front

What does it mean if a system of linear equations has one solution?

Back

The two lines are intersecting lines.

Front

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

Back

The graph consists of parallel lines.

Front

Solve for x and y: 3x + 2y = 16 and 7x + y = 19

Back

(2, 5)

Front

How long does it take Alexandra to do a haircut if 3 haircuts and 2 hair dyes take 315 minutes and 2 haircuts and 4 hair dyes take 450 minutes?

Back

45 minutes.

Front

Which system of equations represents Alexandra's situation: 3 haircuts and 2 hair dyes in 315 minutes, and 2 haircuts and 4 hair dyes in 450 minutes?

Back

3x + 2y = 315 and 2x + 4y = 450.

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean if two lines are parallel in a system of equations?

Back

The system has no solution.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The two lines are the same line.

Front

How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

By analyzing the slopes and y-intercepts of the lines.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable and substituted into the other equation.