# Lesson 119 – Doodles Do Algebra

Today your child starts the next step: solving simple equations for 2 unknowns.

The first point to notice is that in order to solve for 2 unknowns, you need to have 2 independent equations. You can remind your child that independent equations are ones that cannot be simply reduced to be equal. So x=4 and 2x=8 are not inependent since all you have to do is divide the second one by 2 on both sides and you have the same equation. If she is able and willing to engage in a broader discussion of independent equations, you can take the opportunity to show her that $(x-y)^2=3[math] is the same equation as [math]x^2-2xy+y^2=3$ because, as she saw in the course a month ago or so, you can factor the second equation into the first equation.

Ok, so now given that you have 2 independent equations, there are 3 ways to solve them. The first is called Elimination by Substitution and DoodleTwo explains the process very carefully on the worksheet. If this is complex for your child, just walk her through the first problem and then coax her into trying the second one solo. As always, don’t sorry if she won’t do the problem by herself at first. She will keep seeing these types of problems and eventually she will have the confidence to try one by herself. Afterall, you did not just toss her into the pool (I hope) to teach her to swim. You supported her and showed her and coaxed her until she learned the skills and felt confident enough to try them on her own. Why should math be any different?!

1. Step 1: solve the first equation for x. $x=-5y + 30$
Step 2: plug the value for x into the second equation $(y+10)/5-y/3=0$ and solve for y. y=15