Answer:
(15, 10) and (10, 15)
Step-by-step explanation:
The given system of equation is
x + y = 25
xy = 150
To solve the equation, we will use the subtitution method, so first, we need to solve the first equation for y
x + y = 25
x + y - x = 25 - x
x y= 25 - yx
Then, substitute y = 25 - x on the second equation, we get
xy = 150
x(25 - x) = 150
x(25) - x(x) = 150
25x - x² = 150
Now, we can rewrite the equation as
25x = 15 + x²
0 = 150 + x² - 25x
0 = x² - 25x + 150
Therefore, we need to find the values of x that satisfies
x² - 25x + 150 = 0
Now, we need to factorize this equation, so two numbers that multiply to 150 and add to -25 are -15 and -10. Then
(x - 15)(x - 10) = 0
So, the solutions are
x - 15 = 0
x = 15
or
x 10 = 0
x = 10
Then, the values of y are
If x = 15
y = 25 - x
y = 25 - 15
y = 10
If x = 10
y = 25 - x
y = 25 - 10
y = 15
Therefore, the solutions are (15, 10) and (10, 15)
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