Final answer:
The two numbers that multiply to give -7 and add to give 6 are 7 and -1, found by solving the system of equations x * y = -7 and x + y = 6.
Step-by-step explanation:
To find two numbers that multiply to -7 and add to 6, we need to set up a system of equations based on the given conditions. Let's denote the two numbers as x and y. Therefore, we have the following equations:
From the second equation, y can be expressed as 6 - x. Substituting this into the first equation, we get:
x * (6 - x) = -7
Expanding this, we have:
-x^2 + 6x = -7
Adding 7 to both sides, we get:
-x^2 + 6x + 7 = 0
This is a quadratic equation that we can factor as:
-(x - 7)(x + 1) = 0
Setting each factor equal to zero gives us:
Solving for x, we find that the two numbers are 7 and -1.
Therefore, the two numbers that satisfy the conditions are 7 and -1.