CROSS MULTIPLICATION METHOD

This is one of the methods we use to solve system of linear equations.

Let us consider the following system of linear equations.

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

We have to write the coefficients of the equations and do cross multiplication as shown below.

We write the coefficient of y and constant term and two more columns by repeating the coefficients of x and y as follows.

The result is given by

The solution is

Example 1 :

Solve the following system of equations using cross multiplication method :

2x + 7y - 5 = 0

-3x + 8y = -11

Solution :

First we have to change the given linear equations in the form a1x + b1y + c1  =  0, a2x + b2y + c2  =  0.

2x + 7y - 5  =  0

-3x + 8y + 11  =  0

x/(77 + 40) = y/(15 - 22) = 1/[16 + 21]

x/117 = y/(-7) = 1/37

x/117 = 1/37

x = 117/37  

y/(-7) = 1/37

y = -7/37

Therefore the solution is (117/37, -7/37).

Example 2 :

Solve the following system of equations using cross multiplication method :

3x + 4y = 24

20x - 11y = 47

Solution :

Write the given equations in the form of

a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0

3x + 4y - 24 = 0 ----(1)

20x - 11y - 47 = 0 ----(2)

x/(-188 - 264) = y/(-480 - (-141)) = 1/(-33 - 80)

x/(-452) = y/(-480+141)) = 1/(-33-80)

x/(-452) = y/(-339) = 1/(-113)

x/(-452) = 1/(-113)

x = (-452)/(-113)

x = 4

y/(-339) = 1/(-113)

y = (-339)/(-113)

y = 3

Therefore solution is (4, 3).

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Permutation and Combination Problems

    Nov 27, 22 08:59 PM

    Permutation and Combination Problems

    Read More

  2. Combination Problems With Solutions

    Nov 27, 22 08:56 PM

    Combination Problems With Solutions

    Read More

  3. Like and Unlike Fractions Definition

    Nov 26, 22 08:22 PM

    Like and Unlike Fractions Definition - Concept - Examples with step by step explanation

    Read More