Y is 1/3 more than 4 times the value of x

The difference of 3y and 12x is 1.

I agree, you are correct, I took this test already and got an A

difference between the numbers x-y=3

x-y=3 add y on both sides

x-y+y=3+y

x=3+y

square of the smaller number=4 times the larger number

y^2=4*x

y^2=4 (3+y)

y^2=12+4y

subtract 12 and 4y on both sides

y^2-4y-12=12+4y-12-4y

y^2-4y-12=0

on adding - 6 and + 2 we get - 4 and multiplying - 6and 2 we get - 12

y^2 - 4y-12=0 can be written as

y^2-6y+2y-12=0

y (y-6) + 2 (y-6) = 0 here 1st two terms y is common term and last two terms 2 is common term

now y0--6 is common term

(y-6) (y+2) = 0 here equating these two terms with zero we get y value

y-6=0

adding 6 on both sides

y-6+6=0+6

y=6

y+2=0

subtract 2 on both sides

y+2-2=0-2

y=-2

here we take only positive values

y=6 only

now x=3+y=3+6=9

x=9 and y=6

check this problem

difference of these two numbers=9-6=3

two positive numbers differ by 5 means

here positive numbers are x and y

x-y=5

their sum is x+y

square of their sum = (x+y) ^2

(x+y) ^2=169

here 169 can be written as 13^2

(x+y) ^2 = (13) ^2

here powers equal then bases equal

x+y=13 and x-y=5

solving these two equations we get x and y values

x+y=13

x-y=5