I'm just going to start writing the email XD (btw, bold = non-email parts/me talking)
Hey (Friend name),
You kinda missed math the other day, and being the nice friend I am, I decided to catch you up on what we learned.
We learned how to solve a system of equations using the substitution method.
A system of equations is a set of two or more equations with common variables. We use those two equations to solve for the variables.
One example might be:
3x+y=3
4x+3y=10
Solving each of these two equations by themselves would be impossible, so this is where the substitution method comes in.
Solving by substitution means that you first solve one equation for a variable, and then you substitute the value of that variable into the other equation. You might understand better if you see how I use this method to solve the previous system.
Step 1: Solve for y.
3x+y=3
Subtract 3x from each side.
y=3-3x
Step 2: Use the substitution method (plug in the y value).
4x+3y=10
4x+3(3-3x)=10
See how we plugged in the right side of the equation that is equal to y? Now only the x variable is left and we can easily solve it!
Step 3: Simplify to get x.
4x+9-9x=10
-5x=1
x=-1/5
Step 4: Use the substitution method AGAIN (for the y).
Now we plug in the x value into the equation for y.
y=3-3x
y=3-3(-1/5)
y=3-(-3/5)
y=18/5
The final answer is x=-1/5, y=18/5.
As you can see, using the substitution method to solve two impossible equations is how we can get the values of the variables they share! It's simple, quick, and easy!
Sincerely,
(your name)
I hope this helped! :D
