Unique Method for Solving Linear Equations in Two Variables

Introduction: Unique Method for Solving Linear Equations in Two Variables

Hii. I'm sharing a unique method for solving maths equations in 2 variables. As I was solving some them , I thought of experimenting with them to find a new method of my own.
Successfully I found it out :)
I searched on the internet for methods of solving linear equations in two variables. I found 3 of them - substitution method , addition method , Cramer's method , leaving the graphical one. So this one is really different from these.
In other methods , you need certain conditions so that using the methods may solve the equation easily. But this one doesn't need any conditions. It can solve all of them. Let's get started with it !

Step 1: Finding an Equation:

A very simple step. Choose any equation you like. Take a simple one if you are experimenting with it :)
I take it as-
8x+3y=11......(1)
3x-y=2...........(2)

Step 2: Knowing the Way:

This is the main part. In this method , first we find out the value of x in both the equations.
So, 8x+3y=11......(1)
8x=11-3y
x=(11-3y)/8.........(a)
3x-y=2............(2)
3x=2+y
x=(2+y)/3............(b)

Step 3: Solving Them:

As the value of x is same for both the equations, putting (a) and (b) one before the other.
(11-3y)/8=(2+y)/3
Crossmultiplying....
3(11-3y)=8(2+y)
33-9y=16+8y
33-16=8y+9y
17=17y
17/17=y
y=1
Similarly,
Finding the value of y from the equations,
8x+3y=11......(1)
3y=11-8x
y=(11-8x)/3...........(c)
3x-y=2............(2)
-y=2-3x
y=-2+3x.................(d)
Putting ( c) and (d) one before the other,
(11-8x)/3=-2+3x
11-8x=3(-2+3x)
11-8x=-6+9x
11+6=9x+8x
17=17x
17/17=x
x=1

Step 4: Checking It:

You can check it with other methods only to find that this one is much simpler, easier and versatile. I couldn't find a platform for publishing this new method. Thanks to Instructables.
Let me know if you liked it.

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    3 Comments

    0
    kymyst
    kymyst

    1 year ago

    This is just a solution by substitution, not a different method.

    0
    ShivamYadav15
    ShivamYadav15

    Reply 1 year ago

    Hii. This method is totally independent and separate from the others. In substitution method, we find the value of x and substitute in the other equation. Similarly, we find the value of y and substitute in the other equation.
    In this method, we find the value of x from both the equations and equate them. Similarly, we find the value of y from the equations and equate them. This gives us the value of x and y.
    Its hard to solve equations with substitution method which can be solved with addition method. It is not so with this method. Thank you for your question.

    0
    kymyst
    kymyst

    Reply 1 year ago

    I don't agree with you. Equating the x's or y's as you have done is mathematically equivalent to substituting one of the variables. Please consult a mathematics text book if you don't understand why this is so.