Systems of Equations

Front

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

Back

Parallel lines.

Front

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

Back

The two lines are intersecting.

Front

What is the solution to the system of equations represented by the point (1, -1)?

Back

(1, -1) is the solution.

Front

Which system of equations represents David's concession stand sales?

Back

1.5x + 0.5y = 78.5 and x + y = 87.

Front

Which system of equations represents Alexandra's haircuts and hair dyes situation?

Back

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

Front

What are the possible outcomes of a system of equations?

Back

No solution, one solution, or infinitely many solutions.

Front

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

Back

They have no points in common, hence no solution.

Front

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

Back

The two lines overlap, representing the same line.

Front

How can you determine if a system of equations has one solution graphically?

Back

If the lines intersect at a single point.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one equation for one variable.