Question 908655
First lets let y equal one number and x equal the other unknown number.  We need to come up with equations involving x and y.  The first sentence as an equation looks like y = 4x-5.  The other equation would be xy=21.  So now we have a system of equations that we can solve.  I'm going to solve it using substitution.  The system is as follows:<br>

y= 4x-5
xy = 21<br>

Substituting y = 5-4x into the second equation we get:
xy=21
x(4x-5)=21<br>

Now we can solve that equation for x:
x(4x-5) Distribute
4x^2-5x=21 Subtract 21 from both sides
4x^2-5x-21 = 0  Factoring the left hand side
(4x+7)(x-3)=0 Set each factor equal to 0
4x+7 = 0 and x-3 = 0<br>

Solving 4x+7=0:
4x+7=0 Subtract 7 from both sides
4x=-7 Divide both sides by 4
x=-7/4<br>

Since the question specified that both numbers are integers we know that x can not be -7/4th so we eliminate this solution.<br>

Solving x-3=0:
x-3=0 add 3 to both sides
x = 3<br>

Now we can Plug x = 3 into the first equation(y=4x-5) and solve for y:
y=4x-5 Plug in x = 3 
y=4(3)-5 Simplify
y = 12-5 Simplify
y = 7<br>

Checking our work we see that 7 is 5 less than 4 times 3 and that 7*3 is 21.