Question

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

Answer 1

Step-by-step 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 $-3, -4$.

Answer 2

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