Step-by-step explanation:
Let's represent the two integers with the variables [tex]x[/tex] and [tex]y[/tex].
From the problem statement, we can create the following two equations:
[tex]x + y = -7[/tex]
[tex]xy = 12[/tex]
With the first equation, we can subtract [tex]y[/tex] from both sides to isolate the [tex]x[/tex] variable to the left-hand side:
[tex]x = -7 - y[/tex]
Now that we have a value for [tex]x[/tex], we can plug it into the second equation and solve for [tex]y[/tex]:
[tex](-7 - y)y = 12[/tex]
[tex]-7y - y^{2} = 12[/tex]
Now, let's move everything to one side of the equation:
[tex]y^{2} + 7y + 12 = 0[/tex]
Factoring this quadratic will give us two values for [tex]y[/tex]:
[tex](y + 4)(y + 3) = 0[/tex]
[tex]y = -3, -4[/tex]
Since we now know [tex]y = -3, -4[/tex], we can plug this back into either of the original equations to get a value for [tex]x[/tex], which will be [tex]x = -4, -3[/tex].
So the two numbers that sum to [tex]-7[/tex] and have a product of [tex]12[/tex] are [tex]-3, -4[/tex].
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
