SOLUTION: The product of two integers is -21. The difference between the integers is -10. The sum of the two integers is 4. What are the two integers?

Question 922620: The product of two integers is -21. The difference between the integers is -10. The sum of the two integers is 4. What are the two integers?
Answer by josgarithmetic(39626) (Show Source): You can put this solution on YOUR website!
You can almost guess the two numbers from the facts of the description. You know you have signed 7 and 3 but maybe not sure which signs to use.

They are on opposite sides of zero, "difference is -10", but this is badly stated. A difference is never negative! A difference is NOT a signed number and must be understood as POSITIVE.

Sum of the two numbers is 4; meaning 7-3=4,
so no trouble finding the numbers are -3 and 7.

You should go through the exercise of using symbols, or variables, to analyze and find the two integers. The reason is because this is an EASY problem to solve, so knowing what your mistakes may be if you get the wrong result can be identified with little trouble.

SOLUTION USING ASSIGNING VARIABLES
x and y, the two integers.
xy=-21; y-x=10; x+y=4.
Two unknowns and THREE equations.
(y-x)+(x+y)=10+4
2y+0=14
y=7.
Resuming with either of the linear equations,
x+y=4
x=4-y
x=4-7
x=-3.
Just as figured earlier, and also consistant with xy=-21.

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