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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