Algebra II: Systems of Equations

These flashcards cover vital concepts from the lecture on solving systems of equations algebraically, including definitions, examples, and methods.

What is a system of equations?

A system of equations is two or more equations that use the same variables as constraints for a situation.

What is the first equation in Danielle's missile and ray-gun problem?

m + r = 7, where m represents missiles and r represents ray-guns.

What is the second equation in Danielle's problem?

5m + 3r = 23, representing the battery usage of missiles and ray-guns.

What are the three standard methods for solving systems of equations?

Elimination, substitution, and graphing.

What is the solution found when x = 6 and y = 3?

The solution to the system of equations x + y = 9 and x - y = 3.

In the adult and child ticket sales problem, what does a + c = 150 represent?

The total number of adult (a) and child (c) tickets sold.

What does 9a + 6c = 1155 represent in the ticket sales problem?

The total revenue earned from adult and child ticket sales.

If a system of equations results in 0 = 0, what does this signify?

There are infinitely many solutions because the equations represent the same line.

What does it mean if a system results in a false statement like 0 = 9?

There is no solution because the equations represent parallel lines.

How do you convert an equation from standard form to slope-intercept form?

Isolate the y variable on one side of the equation.