Simultaneous equations model

Okay kiddo, so let's say you have two things, let's call them "x" and "y". And you have some information about both "x" and "y".

Let's say that you know that if "x" goes up by 2, then "y" goes up by 3. And you also know that if "x" goes up by 1, then "y" goes down by 2.

This is where a simultaneous equations model comes in handy. You can use this model to figure out the exact values of "x" and "y" that fit these two pieces of information.

To do this, we write the two pieces of information as two equations:

2x + 3y = some number
1x - 2y = some other number

These are the "simultaneous" equations because we are looking at them at the same time.

Now, we want to solve for "x" and "y".

We can use a variety of methods to solve these equations, but one common way is to use something called substitution.

We can solve one of the equations for "x" in terms of "y" or "y" in terms of "x" (doesn't matter which one), and then substitute that value into the other equation.

Let's solve the second equation for "x" in terms of "y":

1x - 2y = some other number
1x = 2y + some other number

Now we can substitute this expression for "x" into the first equation:

2x + 3y = some number
2(2y + some other number) + 3y = some number

Now we have an equation with only "y" in it! We can solve for "y":

4y + some number + 3y = some number
7y + some number = some number
7y = 0

So "y" must equal 0!

Now we can use this value to solve for "x". Let's use the second equation:

1x - 2y = some other number
1x - 2(0) = some other number
1x = some other number

So "x" can be any number we want!

So the values of "x" and "y" that fit the two pieces of information we had are:

x = any number
y = 0

And that's how you use a simultaneous equations model to figure out the values of two things when you have some information about both of them!