Solve the first equation for x, then substitute that value for x in the second equation to find y.

x=y+7
(y+7)*y = 60
y^2 + 7y = 60
y^2 +7y - 60 = 0
(y+12)(y-5)=0 | At this point you probably see the answer, but continue solving for y.

y+12=0 so y=-12
y-5 = 0 so y=5

Only y=5 is valid because the problem specifies positive numbers.

x-y=7 and now we know y=5
x-5=7
x=12

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Answer by Maths68(1474)   (Show Source): You can put this solution on YOUR website!
Let x and y be the two positive numbers
The difference between two positive numbers is 7

.............(1)
Their product is 60

Put the value of x in above equation




Now solve for y



or
or
so

Put the value of y in (1)



x,y= 12, 5



Check
=======
The difference between two positive numbers is 7
12-5=7
7=7
Their product is 60
12*5=60
60=60





Answer by rapaljer(4671)   (Show Source): You can put this solution on YOUR website!
Let x = smaller number
x+7= larger number

x(x+7) = 60
x^2+7x-60=0

If there is a solution to this, then it MUST factor:
(x+12)(x-5)=0
x=-12 Reject, since x must be a positive integer
x=5 Smaller number
x+7 = 12 Larger number

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