Systems of Equations

Front

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

Back

The graph consists of parallel lines.

Front

What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

(2, 5)

Front

What system of equations represents David's concession stand sales if nachos cost $1.50 each and sodas cost $0.50 each, with a total of $78.50 made and 87 items sold?

Back

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

Front

What system of equations represents Alexandra's haircuts and hair dyes if 3 haircuts and 2 hair dyes take 315 minutes and 2 haircuts and 4 hair dyes take 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 for a system of equations to be consistent?

Back

It has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

It has no solutions.

Front

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

Back

The lines intersect at a single point.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable.