Algebra Unit 5 Systems Flashcard Review

Front

If two lines are parallel, they have:

Back

no solutions.

Front

This system has _____ solutions:

Back

no.

Front

If two lines intersect at one point, they have:

Back

one solution.

Front

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?

Back

y = 6.80 + 0.90x and y = 7.30 + 0.65x.

Front

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

Back

(1, 3).

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 have no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the equations represent the same line.

Front

What is the graphical representation of a system of equations?

Back

The point(s) where the lines intersect on a coordinate plane.

Front

How do you determine the number of solutions in a system of equations?

Back

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