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

If x = Erin's age and y = Alex's age, what does the equation x + y = 33 represent?

Back

It represents the total combined age of Erin and Alex.

Front

In the problem 'Erin is 3 years younger than twice Alex's age', how can we express Erin's age in terms of Alex's age?

Back

Erin's age can be expressed as x = 2y - 3.

Front

What does the equation d + c = 50 represent in the context of the donkey and chicken problem?

Back

It represents the total number of donkeys (d) and chickens (c) on the farm.

Front

In the equation 4d + 2c = 174, what do the coefficients represent?

Back

The coefficients represent the number of legs contributed by each type of animal: 4 legs for each donkey and 2 legs for each chicken.

Front

What is the elimination method in solving systems of equations?

Back

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

Front

How can we verify if a solution (-3, -7) is valid for the system y = 4x + 5 and y = x - 4?

Back

Substitute x = -3 and y = -7 into both equations to check if they hold true.

Front

What is the significance of the solution to a system of equations?

Back

The solution represents the point(s) where the equations intersect, indicating the values of the variables that satisfy all equations in the system.

Front

What does the term 'variables' refer to in a system of equations?

Back

Variables are symbols (usually letters) that represent unknown values in equations.

Front

In the context of ticket sales, what do the variables S and C represent?

Back

S represents the number of senior citizen tickets sold, and C represents the number of child tickets sold.