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Answer: -8 and -11
Step-by-step explanation:
Let the first and second numbers be x and y.
Product of the two numbers is 88, therefore:
xy = 88
Sum of the two numbers is -19, therefore:
x + y = -19
Solve simultaneously by first finding y in terms of x in preferably the second equation:
x + y = -19
y = -19-x
Insert y = -19-x in the first equation and solve for x:
x(-19-x)=88
-19x-x²=88
0=x²+19x+88
x²+19x+88=0 (Solve the quadratic equation)
(x+8)(x+11)=0
Therefore x=-8 or x=-11.
Plug in each x in any equations to get y:
When x=-8:
-8+y=-19
y=-11
When x=-11
-11+y=-19
y=-8
∴When x=-8, y=-11 and when x=-11, y=-8
Since in both situations the values of x and y are similar, the two numbers are -8 and -11.