Answer:
x = 8, y = -1
x = -1, y = 8
Explanation:
To find two numbers that multiply to -8 and add up to 15, you can set up a system of equations. Let's call the two numbers x and y:
x * y = -8
x + y = 15
You can solve this system of equations using substitution or elimination. Here's how to use elimination:
From equation (2), you can express one variable in terms of the other:
x = 15 - y
Now, substitute this expression for x into equation (1):
(15 - y) * y = -8
Expand and rearrange:
15y - y^2 = -8
Now, move all terms to one side of the equation:
y^2 - 15y - 8 = 0
This is a quadratic equation. You can solve it using the quadratic formula:
y = [ -b ± √(b² - 4ac) ] / 2a
In this case, a = 1, b = -15, and c = -8. Plug these values into the formula:
y = [ 15 ± √((-15)² - 4(1)(-8)) ] / 2(1)
y = [ 15 ± √(225 + 32) ] / 2
y = [ 15 ± √257 ] / 2
So, you have two possible values for y:
y = (15 + √257) / 2
y = (15 - √257) / 2
Now, you can find the corresponding values for x by using the equation x = 15 - y for each of these y values:
x = 15 - (15 + √257) / 2
x = 15 - (15 - √257) / 2
Simplify each of these expressions to find the corresponding values of x.