System of Equations Word Problems

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that can be solved together.

Front

What does it mean for two equations to intersect on a graph?

Back

It means that the solution to the system of equations is the point where the two lines meet, representing the values of the variables that satisfy both equations.

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, write equations based on the relationships described in the problem, and ensure the equations reflect the total quantities involved.

Front

In the equation x + y = 6, what do x and y represent in a word problem context?

Back

x and y typically represent quantities of different items or groups that add up to a total, in this case, 6.

Front

What is the significance of coefficients in a system of equations?

Back

Coefficients represent the rate or amount associated with each variable in the equations, affecting the total when combined.

Front

How can you check if a solution (x, y) is correct for a system of equations?

Back

Substitute the values of x and y into both equations to see if they satisfy both equations.

Front

What is the first step in solving a system of equations word problem?

Back

Read the problem carefully to identify the variables and the relationships between them.

Front

What does the term 'total receipts' refer to in a word problem?

Back

Total receipts refer to the total amount of money collected from sales, often used to set up an equation in word problems.

Front

How do you set up an equation for a problem involving tickets sold?

Back

Define variables for each type of ticket, write an equation for the total number of tickets, and another for the total revenue generated.

Front

What is the role of the total number of items in a system of equations?

Back

It provides a constraint that helps to form one of the equations in the system.