Solving Linear Systems by Multiplication

Math Scholars, welcome back from Spring Break. We dig right back in to Linear Systems by solving them with multiplication. At this point, all of you have learned many methods to solve systems and multiplication is yet another strategy to add to your skill set.

Emma helped us out today and has clearly demonstrated how to use multiplication to arrange a linear system so it can be solved by addition. The goal is to multiply the entire equation by a number that will create a situation that will cancel either the 'x' or the 'y' when doing addition. If you have any question, be sure to ask during class. Welcome back!

Solving Systems with Addition!

Wow, just when you thought systems were the most difficult, complex problem you have ever solved...you got it! Check out this work by one of my students.

This student is demonstrating how to solve linear systems with addition. As long as there is an x in each system that is the opposite of one another (-8x & 8x), they will cancel and become zero. Therefore, we are then able to solve for y. Once we find y, then -3 is substituted back in for y to solve for x. What a great thing!

Remember, up to this point, this method will only work if you have a situation that allows the cancellation of one of the two variables.