Cross Multiplication Method


Pair of Linear Equations II - Concepts
Class - 10th CBSE Subjects
 
 
Concept Explanation
 

Cross Multiplication Method

CROSS MULTIPLICATION METHOD:

Algorithm to find the solution:

Step 1: Write the given equations in the form :

              large a_{1}x+b_{1}y+c_{1}=0

             large a_{2}x+b_{2}y+c_{2}=0

Step 2: Taking the help of the diagram given below:

 

The arrows between the two numbers indicate that they are to be multiplied and the second product is to be subtracted from the first product.

Write equation as

CROSS MULTIPLICATION METHOD:

Algorithm to find the solution:

Step 1: Write the given equations in the form :

              large a_{1}x+b_{1}y+c_{1}=0

             large a_{2}x+b_{2}y+c_{2}=0

Step 2: Taking the help of the diagram given below:

 

The arrows between the two numbers indicate that they are to be multiplied and the second product is to be subtracted from the first product.

Write equation as

CROSS MULTIPLICATION METHOD:

Algorithm to find the solution:

Step 1: Write the given equations in the form :

              large a_{1}x+b_{1}y+c_{1}=0

             large a_{2}x+b_{2}y+c_{2}=0

Step 2: Taking the help of the diagram given below:

 

The arrows between the two numbers indicate that they are to be multiplied and the second product is to be subtracted from the first product.

Write equation as

EXAMPLE:

1. Solve the two variables linear equation:

8x + 5y = 11

3x – 4y = 10  

Solution:

On transposition, we get

8x + 5y – 11 = 0

3x – 4y – 10 = 0 Writing the co-efficient in the following way, we get:

cross-multiplication, cross multiplication method

By cross-multiplication method:

frac{x}{(5)}(-10)-(-4)(-11) = frac{y}{(-11)}(3)-(-10)(8) = frac{1}{(8)}(-4)-(3)(5)

= frac{x}{-50}-44 = frac{y}{-33}+80 = frac{1}{-32}-15

= frac{x}{-94} = frac{y}{47} = frac{1}{-47}

= frac{x}{-2} = frac{y}{1} = frac{1}{-1} (multiplying by 47)

= x = frac{-2}{-1} = 2     and   = y = frac{1}{-1} = -1

Therefore, required solution is x = 2, y = -1 .      

           

Sample Questions
(More Questions for each concept available in Login)
Question : 1

While solving the pair of linear equations large 2x+3y=46;; &;; 3x+5y=74 using cross multiplication method what will be the value of Z in the relation.large dpi{100} large frac{x}{8}=frac{y}{Z}=frac{1}{1}

Right Option : A
View Explanation
Explanation
Question : 2

While solving the pair of linear equations large dpi{100} large 2x+y=35;; &;; 3x+4y=65 using cross multiplication method what will be the value of Z in the relation.large frac{x}{Z}=frac{y}{25}=frac{1}{5}

Right Option : A
View Explanation
Explanation
Question : 3

While solving the pair of linear equations large 2x+3y=46;; &;; 3x+5y=74 using cross multiplication method what will be the value of Z in the relation.large frac{x}{8}=frac{y}{10}=frac{1}{Z}

Right Option : B
View Explanation
Explanation
 
 
 
Related Videos
Language - English


Students / Parents Reviews [10]