Mathematics is no doubt considered a very difficult & complex subject by many students around the globe. Blame it on the teachers that teach it or the crazy formulas you need to remember.

For all the children who don’t like Algebra & all the other concepts associated with it, we are here to help you with a very important topic of Algebra & that is systems of equations. Let’s look at this concept in more detail!

What exactly systems of equations are?

When you solve two or more equations at the same time or we can say simultaneously, to get the common solution, it is called a system of equations. These equations can be made up of either two or more variables.

To find the accurate solution for both the equations, you need to find a numerical value for each variable in the system, which will be capable of solving/satisfying all equations at the same time.

For example: (6,-1) is the right combination for the following equations:-



Because, when we put the value of x & y as 6 & – 1 in the above equations, the answer comes out to be equal.

2(6)+3(-1)=9               6+4(-1)=2

12-3=9                     6-4=2

9=9                               2=2

What are the various possible ways to solve a system of equations?

To solve any system of equations that are given to you, there are possibly 3 methods to solve them. They are:

  1. Graphical method:

When you solve a system of equations, your solution might have only one set of correct answers or it may have 2 or more. The exact answer will depend on the equation that you are given. 

For equations having one set of correct answers, there will only be a single point of intersection, when plotted at the graph. 

But in case there are two sets of correct answers, there will be two points of intersection on the graph. This will depict that there are two solutions for the equations. 

  1. Substitution method:

One of the easiest methods you will ever come across. In this method, you need to solve your system of equations by expressing your equation in terms of one variable. 

In this, you remove one variable from the equation & put it into another equation, which is hence called substitution. 

  • For example take two equations: 3x+2y=11&   – x+y=3
  • From equation 2, we will find the value of y i.e. y=x+3
  • Now put the value of y in equation 1. It will be, 3x+2(x+3)=11
  • On solving it, the solution will look like this:




5x=5, hence x=1

  • Now we will put this value of x in equation 1. It will be, y=1+3 & therefore, the value of y=4
  • The right set of answers for this system of equations is (1,4)
  1. Elimination method:

In this method, a variable is removed from the system of equations, so that solving the remaining variables becomes easy. Once, the value of other variables is found, then the value of those variables is substituted into the original equation, to find the remaining ones.

  • Take two equations x+y=2 &x-y=14
  • Now eliminate the y variable, by adding up the equations.



2x =16 hence x=8

  • Now, put the value of X in equation 1, it will be 8+y=2
  • Therefore, y=-6. The right pair for this system of equations is (8,-6)

Why study systems of equations online?

Long gone are the days when children used to wait for their teachers, to ask their doubts. This is the era of digitization & hence you can learn everything with the help of the internet. With the help of Cuemath, you can learn online math to help clear your concepts of systems of equations. We provide you with the best subject matter relating to different topics of mathematics. Our team of experts ensures to polish your aptitude skills by supplying you with the best knowledge without spending much.

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