# Lesson 123 of Doodles Do Algebra

Today your child learns how to expand the solving of 2 unknowns using the various elimination techniques he learned last week. Today we do 3 unknowns and 3 equations.

It is essentially the same process as he learned last week. The only difference is that today he has to keep track of which equations he uses as he applies the elimination techniques (substitution, comparison, and addition and subtraction) and make sure to use all three.

If your child seems undaunted by 3 unknowns, let him go at it. There is no one right way of solving this, since you can get at the answer in any number of steps and by applying which ever of the elimination techniques. So if he works it all out then you are golden. If he gets stuck along the way, you need to tease out the point at which he made an error. If that is hard, just ask me in the comments below and I will help you out.

But if he is afraid to start the problem, just walk him through it yourself. Here is how you can do it:

First Step: use elimination by addition to add equation 2 to equation 3 (I chose this because there is a “-z” in equation 2 and a “z” in equation 3 so if you add them together, then the z is cancelled). Here is the result of the addition:

$x+y=15$

Second Step: solve that equation, we just got by elimination by addition in the first step, for x

$x=15-y$

Third Step: substitute the equation we got in the second step into the first original equation. That way we will have “touched” or used all three equations (very, very important) and we will be able to solve for y.

So substituting,

$2(15-y)+y=25$

$30-2y+y=25$

$y=5$

Fourth Step: now it really doesn’t matter which of the original equations you use next. Take the value you found for y (y=5) in the third step above, and substitute it into once of the other equations, we will choose equation 3.

$5+z=10$

$z=5$

Final Step: Now you know that y is 5 and z is 5. So we have a choice of which original equation to use to calculate x (either equation 1 or equation 2). I will choose equation 1 and substitute our calculated value for y and then solve for x.

$2x+5=25$

$2x=20$

$x=10$

Ta-Da!

Final Answer: x=10, y=5, z=5