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What two numbers multiply to give you -35 and add to give you 12

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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.

User Tammye
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