They can, however, be multiplied by any number, just as we had the 3 in our 3x = 30 equation. This means that, for instance, they are not squared x² as in quadratic equations, or the denominator of a fraction, or under a square root. " But what the heck does linear mean?" We say that an equation is linear if its variables (be they x's or coconuts) are to the first power. In essence, " what is the solution to the system of equations." is the same as " give me the value of an apple (or x) that satisfies." To be honest, we know that most scientists would love to use bananas instead of x's, but they're just insecure about their drawing skills. In our case, we know that three apples equal to 30, but the apple is simply a variable, like x, as we don't know the value of it. It denotes a number or element that we don't know the value of, but that we do know something about. The x that appeared above is what we call a variable. However, it doesn't make any difference if you right " Three apples equal to 30," or 3x = 30. " But how? Mathematicians don't use apples and bananas, do they?" Well, they too like to keep the doctor away and bite into an apple from time to time, but you're right, they don't calculate in apples. Want more engaging system of equations lessons? This mini systems of equations unit includes puzzles like these, guided notes, practice and more to help kids make sense of systems.Remember all those riddles on Facebook or Instagram, you know, the ones where three apples are equal to 30, an apple and two bananas are equal to 18, and a banana minus a coconut equal to two, and you had to calculate how much the apple, banana, and coconut are worth? That is what the mathematicians call a system of linear equations. An answer key is included for each puzzle.
Three are “easy” and include a “starting row,” while two are harder, but can be solved, especially if you have older students who can write some equations to represent the rows in the puzzle. These could also be fun challenges for early finishers, or gifted students who enjoy a challenge. This is a great way to get middle schoolers thinking algebraically and using logic and problem solving skills. While this can be a fun way to make a system of equations “not so scary” for Algebra students, these puzzles could be used with younger mathematicians as well! Most students eventually recognize that the key to the puzzle above is to solve for the donut first (because you have three of the same kind-you can divide the cost by 3) and then plug that into the row with just a donut and ice cream, and then use those two solutions to find the cupcake. I simply announce that I have a challenge for them, and the first to correctly solve it wins a prize (or a high five, or bragging rights, etc. I do not say anything about writing equations, solving a system of equations, or anything like that. To help show my students that systems of equations are not all that scary, and actually quite doable, I would start by giving them a “puzzle” to solve, like this one: I would introduce systems of equations with simple and fun puzzle challenges to ease kids in.
Especially if they have struggled to solve a single equation! It doesn’t have to be scary though.
The subject of systems of linear equations is very intimidating to most students.