Question

Reason Abstractly Find two integers whose sum is -7 and whose

product is 12. Explain how you found the numbers.

Answer 1

Answer: -3 and -4

Step-by-step explanation: you can use a system of equations.

x+y=-7

xy=12

Solve for x

x=-7-y

Replace x in the other equation and solve for y

(-7-y)y=12

y^2+7y+12=0

(y+3)(y+4)=0

y+3=0 y+4=0

y=-3 y=-4

Answer 2

Explanation:

Let's represent the two integers with the variables
`x` and
`y`.

From the problem statement, we can create the following two equations:

`x + y = -7`

`xy = 12`

With the first equation, we can subtract
`y` from both sides to isolate the
`x` variable to the left-hand side:

`x = -7 - y`

Now that we have a value for
`x`, we can plug it into the second equation and solve for
`y`:

`(-7 - y)y = 12`

`-7y - y^(2) = 12`

Now, let's move everything to one side of the equation:

`y^(2) + 7y + 12 = 0`

Factoring this quadratic will give us two values for
`y`:

`(y + 4)(y + 3) = 0`

`y = -3, -4`

Since we now know
`y = -3, -4`, we can plug this back into either of the original equations to get a value for
`x`, which will be
`x = -4, -3`.

So the two numbers that sum to
`-7` and have a product of
`12` are
`-3, -4`.