12/18/24 Do Now

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

How do you represent a situation with a system of equations?

Back

You can represent a situation with a system of equations by defining variables for the unknowns and writing equations based on the relationships described in the problem.

Front

What does the variable 'x' typically represent in a problem involving haircuts?

Back

In this context, 'x' usually represents the time taken to give one haircut.

Front

What does the variable 'y' typically represent in a problem involving hair dyes?

Back

In this context, 'y' usually represents the time taken to dye one head of hair.

Front

How do you solve a system of equations?

Back

You can solve a system of equations using methods such as substitution, elimination, or graphing to find the values of the variables that satisfy all equations.

Front

What is the first step in solving the system 3x + 2y = 315 and 2x + 4y = 450?

Back

The first step is to choose a method (substitution or elimination) to isolate one variable.

Front

If 3 haircuts and 2 hair dyes take 315 minutes, how can you express this as an equation?

Back

You can express this as the equation 3x + 2y = 315, where x is the time for one haircut and y is the time for one hair dye.

Front

What is the total time taken for 2 haircuts and 4 hair dyes if it is given as 450 minutes?

Back

The total time taken for 2 haircuts and 4 hair dyes is represented by the equation 2x + 4y = 450.

Front

How do you find the time taken for one hair dye from the equations?

Back

You can solve the system of equations to find the value of 'y', which represents the time taken for one hair dye.

Front

If it takes 90 minutes to dye one head, what is the equation for hair dyes?

Back

If y = 90, then the equation for hair dyes can be substituted into the system to find 'x'.