Cross Multiplication Method Question2





In this page Cross Multiplication Method Question2 we are going to see solution for first problem of the worksheet cross multiplication method.

While solving a pair of linear equations in two unknowns x and y using elimination method,we have to think about how to eliminate any one of the variable in two equations to get value of one unknown and we have to plug it in the second to get the value of other variable. There is another method called cross multiplication which simplifies the procedure.

Solve the following system of equations using cross multiplication method

(ii)  0.5 x + 0.8 y = 0.44 , 0.8 x + 0.6 y = 0.5

Solution:

First we have to make the given equations in the form of a₁ x + b₁ y + c₁ = 0,a₂ x + b₂ y + c₂ = 0.

0.5 x + 0.8 y = 0.44  ----- (1)

0.8 x + 0.6 y = 0.5  ----- (2)

To make the decimal numbers into integers we have to multiply the first equation by 100 and the second equation by 10.

50 x + 80 y - 44 = 0 ----- (1)

8 x + 6 y - 5 = 0  ----- (2)

x/(-400-(-264))  = y/(-352 -(-250))   = 1/(300-640)

x/(-400+264)  = y/(-352+250))   = 1/(-340)

x/(-136)  = y/(-102)   = 1/(-340)

x/(-136)  = 1/(-340)                   y/(-102)   = 1/(-340) 

x = (-136)/(-340)                             y = (-102)/(-340)

         x = 0.4                                       y = 0.3

Therefore solution is (0.4,0.3).

Verification:

Now let us apply the answer that we got in the first or second equation to check whether we got correct answer or not.

0.8 x + 0.6 y = 0.5

0.8(0.4) + 0.6(0.3) = 0.5

0.32 + 0.18 = 0.5

 0.5 = 0.5