Question

There are two numbers. Twice the first number minus the second number equals 18. Twice the second number minus the first number equals 9. Find the numbers

Answer 1

Let's assume

first number is x

second number is y

we are given

Twice the first number minus the second number equals 18

so, we get first equation as

`2x-y=18`

second equation is

Twice the second number minus the first number equals 9

`2y-x=9`

we can solve for y from first equation and plug that in second equation

`y=2x-18`

now, we can plug

`2(2x-18)-x=9`

`4x-36-x=9`

`3x=45`

`x=15`

now, we can find y

`y=2*15-18`

`y=12`

so,

first number is 15

second number is 12..........Answer

Answer 2

Let us suppose the numbers first one is x and second is y

twice the first number - second number = 2x - y =18 -------------( equation 1 )

twice the second number - first number = 2y - x = 9 ------------( equation 2)

let us substitution method for solving these two linear equations .

first equation says 2x- y =18

OR 2x - 18 = y

let us use this value of y in second equation .

second equation is 2y - x = 9

this becomes : 2 ( 2x-18 ) - x = 9

4x - 36 - x = 9

3x = 9 +36

3x = 45

x= 45/3= 15

so y= 2x- 18 = 2( 15) -18 = (30 ) -1 8 = 12

Answer : numbers are 15 and 12