System of equations ?:(
[From: ] [author: ] [Date: 11-11-08] [Hit: ]
x=(1)/…-y^2 − 25x^2 =25x= y^2 − 25solve second equation for y^2 and we gety^2 = x + 25substitute x + 25 for y^2 in first equation and we getx + 25 - 25x^2 = 25- 25x^2 + x = 0x(- 25x + 1) = 0x = 0 or x = 1/25replace x with 0 and 1/25 in one of the two original equations and solve for y. lets choose equation 2 and we get0 = y^2 - 2525 = y^2y = +- 5so (0,5) and (0, - 5)or1/25 = y^2 - 25625/25 + 1/25 = y^2626/25 = y^2+- sqrt(626/25) = y+- 5.004 = yso (1/25, 5.......
Remove the parentheses around the expression (~(626)^(2))/(25).
For y=-(~(626))/(5)_x=((~(626)^(2))/(25))-25
Remove the parentheses from the numerator.
For y=-(~(626))/(5)_x=((1)/(25))-25
Combine -25+(1)/(25) into a single expression by finding the least common denominator (LCD). The LCD of -25+(1)/(25) is 25.
For y=-(~(626))/(5)_x=-(624)/(25)
The final solution is the set of all solutions.
y=5,x=0_y=-5,x=0_y=(~(626))/(5),x=(1)/…
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y^2 − 25x^2 =25
x= y^2 − 25
solve second equation for y^2 and we get
y^2 = x + 25
substitute x + 25 for y^2 in first equation and we get
x + 25 - 25x^2 = 25
- 25x^2 + x = 0
x(- 25x + 1) = 0
x = 0 or x = 1/25
replace x with 0 and 1/25 in one of the two original equations and solve for y. let's choose equation 2 and we get
0 = y^2 - 25
25 = y^2
y = +- 5
so (0,5) and (0, - 5)
or
1/25 = y^2 - 25
625/25 + 1/25 = y^2
626/25 = y^2
+- sqrt(626/25) = y
+- 5.004 = y
so (1/25, 5.004) or (1/25, - 5.004)
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put everything on one side
y^2 - 25x^2 - 25 = 0
-y^2 + x + 25 = 0
add the two
-25x^2 + x = 0
x(-25x+1) = 0
x1 = 0
x2 = 1/25
now calculate y by using the following form of the second one:
y = sqrt(x+25)
and find
y1 = +-5
y2 = +-sqrt(25.04)
so the solutions are
(0,5)
(0,-5)
(1/25, 5.003998401)
(1/25, -5.003998401)
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using the second equation:
y^2=x+25
plug that into the first equation
x+25-25x^2=25
-25x^2+x=0
x=0
0=y^2-25
25=y^2
y=+/-5
(0,5)
(0,-5)
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using the second equation:
y^2=x+25
plug that into the first equation
x+25-25x^2=25
-25x^2+x=0
x=0
0=y^2-25
25=y^2
y=+/-5
(0,5)
(0,-5)
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{x= 0, y = -5},
{x = 0, y = 5},
{x = 1/25, y = -(Sqrt[626]/5)},
{x = 1/25, y = Sqrt[626]/5}
