SOLUTION: urgent....need help? the difference of two numbers is 11, and their product is 42. Find these numbers. choices: a. -14 and 3 b. -3 and 14 c. pair -14 and 3, -3 and 14 d.

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Question 4651: urgent....need help?
the difference of two numbers is 11, and their product is 42. Find these numbers.
choices:
a. -14 and 3
b. -3 and 14
c. pair -14 and 3, -3 and 14
d. pair -14 and 3, 3 and 14
respond asap
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Let the two numbers be x and y:
Then:
x - y = 11 Rewrite this as: x = 11 + y and substitute into the 2nd equation.
xy = 42
(11 + y)y = 42 Simplify.
y^2 + 11y - 42 = 0 Solve by factoring.
(y + 14)(y - 3) = 0 Apply the zero products principle.
y - 3 = 0; y = 3 or
y + 14 = 0; y = -14
x = 11 + y
x = 11 + 3 = 14 or
x = 11 + (-14) = -3
The numbers are: 14 and 3 or -3 and -14
Check:
14-3 = 11 and 14(3) = 42 or
-3-(-14) = 11 and (-3)(-14) = 42