Simultaneous equations

Have you ever heard of equations? They are like math sentences. They tell us about something that we want to know. For example, if we have 5 apples and we want to give 2 apples to our friend, how many apples are left with us? The equation here will be 5 - 2 = ?

Now let's talk about simultaneous equations. Simultaneous equations are like two math sentences that we want to solve together. Just like how we solve one equation, we solve two of them at the same time.

For example, let's say we have two variables - x and y. We have to solve these two equations at the same time -

x + y = 5
2x + y = 8

To solve these, we need to use some magic. We call it "elimination". We have to eliminate one of the variables from one equation so that we are left with only one variable.

We can do that by multiplying or adding/subtracting the equations. Remember, whatever we do to one equation, we have to do the same thing to the other equation too.

In this case, we can eliminate the variable 'y' by multiplying the first equation by -1 and adding it to the second equation.

So, it would look something like this -

(-1)(x + y = 5) -> -x - y = -5

Now we add the two equations -

(-1)(x + y = 5)
2x + y = 8
----------
x = 3

Now that we have found out the value of x from these two equations, we can use it to find out the value of y. We substitute the value of x in any of the two equations we had before. Let's use the first one.

x + y = 5
3 + y = 5

Now we subtract 3 from both sides of the equation -

y = 2

So the solution to these two equations is x=3 and y=2.

So, basically, simultaneous equations are two equations that we solve together to find out the values of the variables. We use elimination to get rid of one variable and find out the value of the other variable.