*Many of our resources are part of collections that are created by our various research projects.*

*Many of our resources are part of collections that are created by our various research projects.Each collection has specific learning goals within the context of a larger subject area.*

Trying to solve two equations each with the same two unknown variables?

Take one of the equations and solve it for one of the variables.

This is where I get the headings on the tables below. There are twice as many nickels as pennies, so there are nickels. Be sure you understand the equations in the pennies and nickels rows are the way they are: The number of coins times the value per coin is the total value. This might be the total cost of a number of tickets, the distance travelled by a car or a plane, the total interest earned by an investment, and so on.

You'll see that the same idea is used to set up the tables for all of these examples: Figure out what you'd do in a particular case, and the equation will say how to do this in general. If there are twice as many nickels as pennies, how many pennies does Calvin have? In this kind of problem, it's good to do everything in cents to avoid having to work with decimals. If the words seem too abstract to grasp, try some examples: If you have 3 nickels, they're worth cents. With this arrangement: There are many correct ways of doing math problems, and you don't have to use tables to do these problems.

If the equations are all linear, then you have a system of linear equations!

To solve a system of equations, you need to figure out the variable values that solve all the equations involved. This tutorial will take you through this process of substitution step-by-step!A system of equations is a set of equations with the same variables.If I have 6 tickets which cost each, the total cost is If I have 8 dimes, the total value is This is common sense, and is probably familiar to you from your experience with coins and buying things.But notice that these examples tell me what the general equation should be: The number of items times the cost (or value) per item gives the total cost (or value). The total value of the coins (880) is the value of the pennies will go in the third column.Then plug that into the other equation and solve for the variable.Plug that value into either equation to get the value for the other variable.Typically, one equation will relate the number of quantities (people or boxes) and the other equation will relate the values (price of tickets or number of items in the boxes). To review how this works, in the system above, I could multiply the first equation by 2 to get the y-numbers to match, then add the resulting equations: If I plug into , I can solve for y: In some cases, the whole equation method isn't necessary, because you can just do a substitution. The first few problems will involve items (coins, stamps, tickets) with different prices.But they are convenient for organizing information --- and they give you a pattern to get started with problems of a given kind (e.g.interest problems, or time-speed-distance problems). In some cases, you the numbers in some of the columns in a table.

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