Answer:
-14
Step-by-step explanation:
a + b = -19
(a)(b) = 70
To solve this problem, isolate one variable in one of the two equations and then substitute it in.
So, a + b = -19
-> a = -19 - b
b(-19 - b) = 70
Distribute.
-19b - b^2 = 70
Move all to one side.
b^2 + 19b + 70 = 0
Factor. Find two numbers that multiply to 70, but add to 19.
(b + 5) (b + 14) = 0
Zero product rule.
b = -5, b = -14
Now, substitute the two answers for b back into the original equation for a.
a - 14 = -19
a = -5
a - 5 = -19
a = -14
So, the answers are b = -5, b = -14, a = -5, a = -14. Since you said that the smallest integer is the answer, the answer is -14.
