12.4-5 System of Equations Word Problems Day 1

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 if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean if a system of equations has one solution?

Back

It means that the equations represent lines that intersect at exactly one point.

Front

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

Back

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

Front

How do you represent the total number of items in a system of equations?

Back

By using an equation that sums the quantities of the variables, such as x + y = total.

Front

How do you represent the total cost in a system of equations?

Back

By using an equation that sums the products of the quantities and their respective prices, such as 20x + 50y = total cost.

Front

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

Back

Identify the variables and what they represent in the context of the problem.

Front

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

Back

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

Front

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

Back

They represent the rate of change or the weight of each variable in the context of the problem.

Front

What is a common method for solving systems of equations?

Back

Substitution or elimination methods are commonly used to find the solution.