Find two numbers whose sum is -12 and whose product is 11

Answer 1

x + y = -12

xy = 11

We need to use substitution, so get one equation in terms of x

x = -12 - y

then plug in for x in the other equation

(-12 - y)y = 11

-12y - y² = 11

y² + 12y + 11 = 0

(y + 11)(y + 1) = 0

y = -11 or y = -1

when y = -11:

x + (-11) = -12

x = -1

when y = -1

x + (-1) = -12

x = -11

so the two numbers are -1 and -11

Answer 2

From the Problem, we know that x+y=-12 and x*y=11

So we list the numbers that if we multiply them we get 11

1*11=11

-1*-11=11

Then we take both pairs of numbers and add them together to see which one equals -12

1+11=12

-1+-11=-12 <-------- This is the correct answer.

Answer 3

1) Write out what you know.

x + y = -12

xy = 11

2) Solve one of the equations for one variable.

y = -12 - x

3) Plug that expression into the other equation, multiply it out, and simplify.

x*(-12 - x) = 11

-12x - x^2 = 11

-x^2 - 12x - 11 = 0... if you multiply the whole expression by -1, you get:

x^2 + 12x + 11 = 0

(x - 1)(x - 11) = 0

x = -1, x = -11