Question

What two numbers, when multiplied, equal -18 but also, when added together, equal 17?

Answer 1

To find two numbers that satisfy the given conditions, set up a system of equations and solve. The two numbers that satisfy the conditions are 18 and -1, or -1 and 18.

Step-by-step explanation:

To find two numbers that satisfy the given conditions, we can set up a system of equations.

Let's call the two numbers x and y. We are given the following conditions:

1. x * y = -18
2. x + y = 17

We can solve this system of equations by substitution or elimination. Let's use the substitution method:

1. From the second equation, we can solve for y: y = 17 - x
2. Substitute this expression for y in the first equation: x * (17 - x) = -18
3. Expand and simplify the equation: 17x - x^2 = -18
4. Rearrange the equation: x^2 - 17x - 18 = 0
5. Factor the quadratic equation: (x - 18)(x + 1) = 0
6. Solve for x: x = 18 or x = -1
7. Substitute these values of x back into the second equation to find y:

If x = 18, then y = 17 - 18 = -1

If x = -1, then y = 17 - (-1) = 18

Therefore, the two numbers that satisfy the given conditions are 18 and -1, or -1 and 18.