the sum of two numbers are 61 and the difference is 11

Answer 1

let' x=the first number' and 'y=the second number'

since the two numbers add to 61 we can write this as:

x+y=61

since their difference is 11:

x-y=11

now solving the system of equations:

1) isolate 'x' in the second equation

x=11+y

2)apply the substitution for' x+y=61':

11+y+y=61

3)solve for y

11+2y=61

2y=50

y=25

so the second number is 25.

4) plug in for y in either equation to find x:

x+25=61

x=36

so the first number is 36

so the numbers that satisfy the conditions is 36 and 25