Final answer:
To find two numbers that multiply to give -35 and add to give 12, we can set up a system of equations and solve them using different methods. In this case, using the substitution method, we find that the two numbers are 7 and -7, or 19 and 5.
Step-by-step explanation:
To find two numbers that multiply to give -35 and add to give 12, we can set up a system of equations.
Let's call the two numbers x and y.
From the given information, we have the following equations:
x * y = -35
x + y = 12
Now, we can solve these equations using different methods such as substitution or elimination. Let's use the substitution method.
From the second equation, we can express x in terms of y:
x = 12 - y
Substituting this value of x into the first equation, we have:
(12 - y) * y = -35
Expanding and rearranging the equation, we get:
y^2 - 12y - 35 = 0
Now we can solve this quadratic equation for y. Factoring or using the quadratic formula, we find that:
y = 5 or y = -7
Substituting these values of y back into the second equation, we can find the corresponding values of x:
If y = 5, then x = 12 - 5 = 7
If y = -7, then x = 12 - (-7) = 19
So, the two numbers that multiply to give -35 and add to give 12 are 7 and -7, or 19 and 5.