# Systems of Equations Introduction

Last year, I was really struggling to teach my Algebra 1 students how to solve a system of equations using substitution. This struggle completely flabbergasted me, because substitution always made so much sense to ME and I found elimination to be harder, while my students LOVED elimination and couldn’t comprehend substitution at all.

“What do you mean, ‘substitute’?” “(Seriously? We’ve been substituting things into equations all year! I can’t even say the word properly anymore because I’ve said it so much!)

“So, I put the other equation here?” (Then they replace the y with the whole equation y=3x so now they have two equal signs.) (Their other favorite thing was to leave the original variable in the equation, so now their new equation says y3x.)

They adored elimination. It was their favorite thing ever. They started adding equations together on problems that didn’t even have a system. Of course, they really struggled to remember to multiply the equation before adding when they didn’t have equal coefficients…but their equation-solving skills were so atrocious that they could somehow still manage to lose the variable they had not actually eliminated…and now I’m just getting frustrated all over again so I’m going to go back to my original point.

Ahem. So I was looking around online last year for a different way to approach teaching substitution as a method for solving systems, and I ran across two ideas, both of which I’m using this year. I’m only going to discuss one of them in this post, because I need to go to bed. I’ll write up my thoughts on the other one later, after I actually implement it next week or the week after. Continue reading