Q. 185.0( 2 Votes )

Solve for x and y

Answer :

We are given with a matrix equation,


We need to find x and y.




These matrices can be added easily as they are of same order.



If two matrices are equal, then their corresponding elements are also equal.


This implies,


2x + 3y – 8 = 0 …(i)


x + 5y – 11 = 0 …(ii)


We have two variables, x and y; and two equations. It can be solved.


Rearranging equation (i), we get


2x + 3y = 8 …(iii)


Rearranging equation (ii), then multiplying it by 2 on both sides, we get


x + 5y = 11


2(x + 5y) = 2 × 11


2x + 10y = 22 …(iv)


Subtracting equation (iii) from (iv), we get


(2x + 10y) – (2x + 3y) = 22 – 8


2x + 10y – 2x – 3y = 14


2x – 2x + 10y – 3y = 14


7y = 14



y = 2


Substituting y = 2 in equation (iii), we get


2x + 3(2) = 8


2x + 6 = 8


2x = 8 – 6


2x = 2



x = 1


Thus, x = 1 and y = 2.


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