SOLUTION: what two numbers add to negative 6 and multiply to negative 91

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Question 1003316: what two numbers add to negative 6 and multiply to negative 91
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let two numbers be x and y
if they add to negative 6, we have
x%2By=-6..........eq.1
and if they multiply to negative 91, we have
x%2Ay=-91..........eq.2
solve the system:
x%2By=-6..........eq.1
x%2Ay=-91..........eq.2
-----------------------------
start with x%2By=-6..........eq.1, solve for x
x=-6-y....substitute it in eq.2 and solve for y
%28-6-y%29%2Ay=-91..........eq.2
-6y-y%5E2=-91
0=y%5E2%2B6y-91
0=y%5E2%2B6y-91 ......factor completely
0=y%5E2-7y%2B13y-91
0=%28y%5E2-7y%29%2B%2813y-91%29
0=y%28y-7%29%2B13%28y-7%29
0=%28y%2B13%29%28y-7%29
solutions:
if 0=%28y%2B13%29=>y=-13
if 0=%28y-7%29=>y=7
now find x
x%2By=-6..........if y=-13
x-13=-6
x=-6%2B13
x=7

x%2By=-6..........if y=7
x%2B7=-6
x=-6-7
x=-13
so, your numbers are:

x=7 and y=-13
or
x=-13 and y=7