math word problem (2 variables) 1 question only.. please help me.. difficult for ME!!?

"the sum of two numbers is 60"

this implies addition, the existence of 2 numbers and the combination being 60

since we do not know these 2 numbers, we will use variables: x & y

so we have

x + y = 60

"and their difference is 8"

this implies usage of the same 2 numbers, subtraction and the combination being 8

so we have

x - y = 8

now we have 2 equations

x+y=60

x-y=8

1st, let x or y be alone, in any equation, for me, i would prefer to leave x alone in the 1st equation

x + y = 60

x + y - y = 60 - y

x = 60 - y

Though this is not a number, we do have a value for x

we use this value to substitute in the next equation

x - y = 8; x = 60 - y

(60 - y) - y = 8

60 - y - y = 8

60 - 2y = 8

60 - 60 - 2y = 8 - 60

- 2y = - 52

y = (-52)/(-2)

y = 26

but we do not have x yet

so, we use any of the 2 equations to get the value of x:

x - y = 8; y = 26

x - 26 = 8

x - 26 + 26 = 8 + 26

x = 8 + 26

x = 34

or

x + y = 60

x + 26 = 60

x + 26 -26 = 60 -26

x = 60 - 26

x = 34

either way, we get 34 for x, thus

x = 34 and y = 26

(hope this helps)

Let us assume the two numbers to be x and y ( where x>y)

now, given that

x + y = 60

and x - y = 8

now adding the two equations, we get

x + x + y - y = 68

= 2x + 0 = 68

= x = 68/2

= x= 34

= from equation x-y = 8

34-y =8

= -y= 8 - 34

= -y = -26

= y = 26

solution x = 34 y = 26

x + y = 60

y = 60 - x

x - y = 8

y = x - 8

1st number (x):

60 - x = x - 8

2x = 68

x = 34

2nd number:

= 60 - 34

= 26

Answer: 34 and 26 are the numbers. Their sum is 60.

Proof (difference is 8):

= 34 - 26

= 8

x + y = 60

x - y = 8

so 2x = 68

so, x = 34 and y = 60-34

= 26

Let the greater number be x and let the smaller number be y.

So,

x+y = 60 -----(1)

x-y = 8 -------(2)

(1)+(2): 2x=68

x=68/2

x=34

(1)-(2): 2y=52

y=52/2

y=26

Therefore, the numbers are 34 and 26.

x = one number

y = second number

SUM means to Add

DIFFERENCE means to Subtract

The equations:

x + y = 60

x - y = 8

Add the two equations together and your y's will cancel

x + y = 60

x - y = 8

------------------

2x = 68

Divide both sides by 2 and you will solve for 'x''

x = 34

Now, plug in the 34 for x in x + y = 60

x + y = 60

34 + y = 60

Subtract 34 from both sides and you will solve for ''y''

y = 26

CHECK:

34 + 26 = 60

60 = 60

34 - 26 = 8

8 = 8

It works! Go for it!

Best wishes!

x=34

y=26

the steps:

let the first no=x ,let the second no=y

x+y=60

x-y=8

then we will add x+y and x-y the result will be 2x then we will add 60+8 the result will be 68

2x=68

then X=34

after that we will subistitute with the variable x we will get the variable y

x + y = 60

x - y =8

add them up

2x = 68

x=34

plug x back in, 34 - y = 8

x=34, y=26

let the nos be x & y

now x+y = 60

and x-y = 8

adding both eqns

2x = 68; x=34

subtracting second eqn from first

2y = 52; y=26

x+y=60 and x-y=8

adding them...

x+y=60

+ x-y=8

y will cancel out so

x=34

and y= 26