Question

One number is 2 more than another. The difference between their squares is 24.

Answer 1

Answer: The numbers are 7 and 5

Step-by-step explanation:

Let the first number be x and the second number be y.

From the first statement , it was said that one of the number is two more than the other , that is

x - y = 2  .................. equation 1

square of x is $x^{2}$ and the square of y is $y^{2}$ , the difference between thier squares implies

$x^{2}$ - $y^{2}$ = 24 .............. equation 2

solving the resulting simultaneous equations by substitution method:

From equation 1 , make x the subject of the formula , that is

x = 2 + y ............. equation 3

substitute equation 3 into equation 2 , we have

$(2+y)^{2}$ - $y^{2}$ = 24

Expanding , we have

$y^{2}$ + 4y + 4 - $y^{2}$  = 24

4y + 4 = 24

Subtract 4 from both sides

4y = 20

y = 20/4

y = 5

substitute y = 5 into equation 3 , we have

x = 5+ 2

x = 7

Therefor the numbers are 7 and 5

Answer 2

Answer: x = 7; y = 5

Step-by-step explanation:

Let's call the first number x and the second number y so we can form a system in which:

x - y = 2  

x²   -   y² = 24

isolating x from the first equation:

x = 2 + y

replacing x that is worth 2 + y in the second equation

(2 + y)²  -  y²  = 24

4 + 2 . 2 . y +  y²  - y²  = 24

4 + 4y = 24

4y = 24 - 4

4y = 24

y =  20/4  

y = 5

substituting the y that is worth 5 in the first equation:

x - y = 2

x - 5 = 2

x = 2 + 5

x = 7

I hope this help