Subtracting the second equation by 18 on both sides, we have xy=-18. Next, we divide both sides by x to get y=-18/x Plugging that into the first equation, we have x+2(-18/x)=9. Multiplying both sides by x, we get x^2-36=9x. After that, we subtract both sides by 9x to get x^2-9x-36=0. Finding 2 numbers that add up to -9 but multiply to -36, we do a bit of guess and check to find the answers to be -12 and 3. Factoring it, we get
x^2-12x+3x-36=x(x-12)+3(x-12)=(x+3)(x-12). To find the x values, we have to find out when 0=(x+3)(x-12). This is simple as when you multiply 0 with anything, it is 0. Therefore, x=-3 and 12. Plugging those into x=-18/y, we get x=-18/y and by multiplying y to both sides, we get xy=-18 and then we can divide both sides by x to get -18/x=y. Plugging -3 in, we get -18/-3=6 and by plugging 12 in we get -18/12=-1.5. Therefore, our points are (-3,6) and (12, -1.5)
Answer:
A = (-1,5) or (-1,-3)
Step-by-step explanation:
A = (-1,y) B = (2,1)
(Distance from A to B) = √[(-1-2)² + (y-1)²] = 5
=√[9 + y² - 2y + 1] = 5
Squaring on both sides
= y² - 2y + 10 = 25
=y² - 2y -15 = 0
= (y-5)(y+3) = 0
y = 5 or -3
Therefore, A = (-1,5) or (-1,-3)
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