Question

One fifth of the difference of two numbers is 3 and one third of their sum is 7. Find
the numbers by using matrix method.​

Answer 1

lets the numbers be x,y

we know,

(x - y)/5 = 3

=> x - y = 15 - (1)

(x + y)/3 = 7

=> x + y = 21 - (2)

We can use substitution or elimination to solve this, I am going to use substitution.

From (1)

x = 15 + y

In (2)

(15 + y) + y = 21

=> 15 + y + y = 21

=> 2y = 6

=> y = 6/2

=> y = 3 - (3)

Replacing (3) in (1)

x - 3 = 15

=> x = 12

Therefore, x = 12, y = 3.

Have a nice day!