Using a system of equations, the numbers that add to 1 and multiply to -72 are given as follows:
9 and -8.
<h3>What is a system of equations?</h3>
A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable.
In the context of this problem, the two numbers are the variables. They are unknown, hence they are going to be defined as follows:
x and y.
They add to 1, hence:
x + y = 1.
They multiply to -72, hence:
xy = -72.
From the first equation, we have the following relation:
y = 1 - x.
Replacing in the second, we have that:
x(1 - x) = -72.
x - x² = -72.
x² - x - 72 = 0.
The quadratic function can be factored as follows:
(x - 9)(x + 8) = 0.
Hence the amounts are given as follows:
Which are the two numbers representing the solution to the system of equations.
More can be learned about a system of equations at brainly.com/question/24342899
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