Find two postive integers whise difference is 1 and the difference of their squares is 5

Question

Please i need to understand how to solve it asap because I’m going to report about it tomorrow.

Answer 1

The equations for what is described are:

x-y=1

x²-y²=5

Next, need to solve. We can solve by substitution. Solving the first equation for y,

y=x-1 Then need to plug this into the second equation.

x²-(x-1)²=5 FOIL the second term

x²-(x²-2x+1) = 5 Distribute the -1 to each term to clear the parenthesis

x²-x²+2x-1 = 5 Combine like terms

2x-1 = 5 Add 1 to both sides

2x-1+1 = 5+1 Simplify

2x = 6 Divide both sides by 2

2x/2 = 6/2

x=3

Now can plug this into the first equation to get y

y=x-1

y=3-1

y=2

The solution is (3,2) If you plug this into both equations, it will work