The beginning of my landmark journey in mathematics all began when I was finally able to unravel a simple secret that understanding fundamentals is the key to solving any mathematical problem. And of course, that was all I needed at that point to step up my reasoning and my understanding of complex phenomenons. But before I was able to unravel this secret, mathematics was a nightmare that always ignites the fear in me.
Having gone through this as a student, I know exactly how it feels to find it difficult to understand mathematics. With that in mind, I have found ways to bridge the gap between students and the fundamentals of mathematics which is the most important part of this subject. At this point, I will be taking a thorough guide on solving a system of equations.
After this guide, am sure that students that can go through this will no longer find those x’s and y’s eye-crossing. Rather, they will be able to take inference from this guide solve whatever system of equations that comes their way.
But before we take any step forward, let’s first glance through what system of equations means and the important roles it has to play in mathematics as a fundamental.
What is a System of Equations?
Just as its name implies, a system of equations has to do with solving two or more linear equations together. In other words, we will be having an x-variable, y-variable, and constant value. For more complicated systems of equations, there are usually the higher-order functions such as the quadratic functions.
Irrespective of how complicated the system is, it is being solved primarily with the aid of an intersection. Which has to do with the intersection between two different lines on a point. But in the case of parallel lines where there are no intersections, an equation can’t be formed.
How to solve a system of equations?
When it comes to solving a system of equations, three principal methods are used. These include a graphical method, substitution method, and elimination method. Each of these methods can be used to solve a system of equations in several ways. Let’s take a step further by explaining each of these methods.
- The Graphing Method – This is the easiest way to solve a system of equations. This method involves finding the intersection of a system on the same coordinate plane. Although, the results from this method is often irregular. Hence, we have other methods below for solving a system of equations.
- The Substitution Method – This method involves a simple process called substitution of variables. Here, what I do is isolate the variable of one of the equations to find the other variable. With the value of one of this variable known, I will easily find the value of the other variable.
- The Elimination Method – This another simple method. The basic step here is to eliminate the variable of one of the equation to find the other value. To get this done, all I need to do is multiply both or one of the equations by a constant value
As we all know solving a system of equations are a big part of the math sections of the SAT. You can prepare for the SAT at Caddell Prep if you need further explanation about this topic.
