Systems of Equations (All three methods)

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations that have the same variables.

Front

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

Back

Get either variable by itself.

Front

What does the elimination method involve?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the value of the y-coordinate of the solution to the system of equations: x - 2y = 1 and x + 4y = 7?

Back

1

Front

What is the reasonable domain for Leslie's car that travels about 25 miles per gallon and needs 14 gallons of gas to be full?

Back

0 ≤ x ≤ 14

Front

Write an equation for the amount of money Derrick raises, A, if he sells x amount of leashes, given it costs him $120 to get supplies and he sells each leash for $5.

Back

A = -120 + 5x

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the point(s) where the lines of the equations intersect.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines are parallel and do not intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, and every point on the line is a solution.

Front

How can you check if a solution is correct for a system of equations?

Back

Substitute the solution back into the original equations to see if they hold true.