4.4 Systems Word Problems

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 word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and express them as a system.

Front

What does it mean for two companies to have the same cost?

Back

It means that the total cost equations for both companies are equal at a certain number of toppings.

Front

If a pizza costs a base price plus a topping price, how can you express this mathematically?

Back

Let y be the total cost and x be the number of toppings. The equation is y = base price + (topping price * x).

Front

What is the sum of two numbers?

Back

The sum is the result of adding the two numbers together.

Front

What is the difference between two numbers?

Back

The difference is the result of subtracting one number from another.

Front

How can you express the relationship between two numbers in equations?

Back

If x and y are the two numbers, their sum can be expressed as x + y = sum and their difference as x - y = difference.

Front

What is a variable in a system of equations?

Back

A variable is a symbol used to represent an unknown value in equations.

Front

How do you solve a system of equations graphically?

Back

You graph each equation on the same coordinate plane and find the point(s) where they intersect.

Front

What does it mean to solve a system of equations algebraically?

Back

It means to manipulate the equations using algebraic methods to find the values of the variables.