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Learning Linear Variables in Two Variables Easily


Introduction
Equations pave the way towards learning algebra. While learning equations, you will constantly learn about linear equations, particularly linear equations in one variable and linear equations in two variables. In this blog, we will be discussing linear equations in two variables.

Linear Equations In Two Variables
The concept of linear equations are known for being tough for students across the nation, many people also end up the search for “tuition for class 9 near me”. However, it isn’t as complicated as it is presumed to be. In fact, after learning from this blog, you won’t even have to search for any math tutor near me.
 Linear equations are simply expressed as:
ax + by + c = 0
In this equation, a, b, and c and all real numbers which are not equal to 0. The solutions derived for x and y make both sides of the equation equal.

Solving Equations In Two Variables
There are two ways by which linear equations in two variables can be solved. These are by:
·         The Substitution Method
·         The Elimination Method

The Substitution Method
In the substitution method, one of the equations is solved for one of the variables. The answer is substituted into the other equation to yield a value which is again substituted back into the first equation to find the other value.
Problem: 2x – 2y – 4= 0 and 2x + 2y – 8 = 0
Step 1: Start by substituting one variable over to the right-hand side in one equation.
ð  2x – 2y – 4 = 0
ð  2x – 4 = 2y
ð  2y = 2x – 4
ð  y = x – 2

Step 2: Now substitute this value into the other equation.
ð  2x + 2(x – 2) – 8 = 0

Step 3: Now solve this.
ð  2x + 2x – 4 = 8
ð  4x = 12
ð  x = 3

Step 4: Now put this value back into the first equation to get the value of y.
ð  2x – 2y = 4
ð  6 – 2y = 4
ð  2y = 6 – 4
ð  y = 1

Therefore, x = 3 and y = 1.

The Elimination Method
The second method is the elimination method. This method involves multiplying both the equations by appropriate numbers (if needed) for the same coefficient of variables. Both equations are then added to receive a single value. This answer is then substituted within one of the equations to find the other answer.
Let’s use the same example for the answer: 2x – 2y – 4 = 0 and 2x + 2y – 8 = 0
Step 1: Arrange both the equations one beneath the other.
ð  2x – 2y – 4 = 0
            2x + 2y – 8 = 0

Step 2: Upon adding these equations, we get:
ð  4x = 12

Step 3: Solving this, we get:
ð  x = 3

Step 4: Substitute this value into another equation to get the value of y:
ð  2x + 2y – 8 = 0
ð  2(3) + 2y = 8
ð  6 + 2y = 8
ð  2y = 8 – 6
ð  y = 1

Therefore, x = 3 and y = 1. 

Conclusion:
You don't have to worry about maths anymore, there are tutors and sample papers which will help you learn maths in the simplest way possible. Even while preparing for maths examination you'll be confident and assured to clear the examination with flying colors. You would be the only person with so much confidence while solving the paper than all people inside the examination hall.



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