# Creating a table from a system of linear equations

• armolinasf
In summary, the conversation discusses creating a table to show possible combinations of three liquids containing different percentages of vitamin c and d that can be used to fill a doctor's prescription calling for a daily intake of 40mg of vitamin c and 30mg of vitamin d. The solution involves setting up a system of linear equations with three variables, representing the amount of liquid taken from each type, with grams as the chosen unit. The amounts of vitamins can then be expressed in terms of these variables to solve the system.
armolinasf

## Homework Statement

A doctor's prescription calls for a daily intake of liquid containing 40mg of vitamin c and 30mg of vitamin d. There are three liquids that can be used: one contains 20%vitamin c and 30% vitamin d; the second, 40% vitamin c and 20% vitamin d; the third, 30% vitamin c and 50% vitamin d.

Create a table showing the possible combinations that could be used to fill the prescription.

## The Attempt at a Solution

I'm not quite sure how to approach this one. I'm thinking of setting it up as a system of linear equations with three variables. I'm having trouble relating the percentages to the amount in grams. Thanks for the help.

That sounds like a good idea. The three variables you would use (let's call them x, y, z) would then correspond to the amount of liquid you take from each of the three types.
I would choose grams as units for x, y, z; so for example x = 120 corresponds to taking 120 g of liquid one. Then you can easily express the amount of vitamins in terms of x, y and z and draw up your system of equations.

## What is a system of linear equations?

A system of linear equations is a set of two or more equations that contain one or more variables. The solutions to these equations are the values that make all of the equations true simultaneously.

## How do I create a table from a system of linear equations?

To create a table from a system of linear equations, choose values for one variable and use them to solve each equation for the other variable. Then, list the corresponding values for each variable in the table. Repeat this process for different values of the first variable to create a table of solutions.

## What is the purpose of creating a table from a system of linear equations?

A table can help visualize the relationship between the variables in a system of linear equations. It can also be used to identify patterns and determine the solution to the system by finding the values that make all of the equations true.

## How do I know if a table represents a solution to a system of linear equations?

If the values listed in the table make all of the equations in the system true, then the table represents a solution to the system. It is important to check that all of the equations are satisfied by the table values, as a single incorrect value can make the entire solution invalid.

## What are some common methods for solving a system of linear equations?

Some common methods for solving a system of linear equations include graphing, substitution, and elimination. Each method has its own advantages and may be more suitable for different types of problems. It is important to choose a method that is most efficient for the given system.

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