Question

There are two numbers such that sum of twice the 1st nmbr and thrice the second number is 100 and the sum of thrice the 1st number and twice the second number is 120 .whuch is the largest number

Answer 1

let fist no be x
2nd no be y

as per qstn 2x+3y=100
x=(100-3y)/2......value of x

3x+2y=120
3(100-3y)/2+2y=120
300-9y+4y=120*2
5y=300-240
y=60/5
=12

Answer 2

Let the numbers are x and y

2x+3y=100

3x+2y=120

multiply top by 3 and bottom by +2

6x+9y=300........[1]

6x+4y=240.........[2]

sbtracting equation [1] and [2] we get

5y=-60

y=12

putting the value of y=12 in equation [1]  we get

2x+3(12)=100

2x+36=100

2x=64

x=32

check in second equation

3(32)+2(12)=96+24=120

numbers are (32 and 12)  ans    first nos is largest