Systems of Equations - 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 set them equal to each other.

Front

What does it mean for two companies to charge the same amount?

Back

It means that the total cost from both companies is equal, which can be represented by setting their cost equations equal to each other.

Front

What is the setup fee in a cost equation?

Back

The setup fee is a fixed cost that is added to the total cost of items purchased, regardless of the quantity.

Front

How do you find the solution to a system of equations graphically?

Back

Plot both equations on a graph and identify the point(s) where they intersect. This point represents the solution.

Front

What does the slope of a line represent in a word problem?

Back

The slope represents the rate of change or how much one variable changes in relation to another.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is zero; it represents the starting point of the line on the y-axis.

Front

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

Back

Substitute the solution back into both equations to see if it satisfies both.

Front

What is a reasonable solution in the context of a graph?

Back

A reasonable solution is a point on the graph that makes sense in the context of the problem, such as non-negative quantities.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have the same slope and will never intersect, indicating no solution to the system.