anonymous
  • anonymous
solve this quadratic system: 4x^2 + 9y^2 = 72 x - y^2 = -1 explain please?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
they want to know what points they have in common
amistre64
  • amistre64
-72 from each side of the top one and +1 to both sides of the bottom one and you will have 2 equations equal to 0
amistre64
  • amistre64
since both equation = 0; they equal each other; so make them equal and subtract one equation from the other

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amistre64
  • amistre64
4x^2 + 9y^2 -72 = x - y^2 +1 4x^2 + 9y^2 -72 -x + y^2 -1 ---------------- 4x^2 -x +10y^2 -73 = 0 but i might be trying to do this the ahard way
amistre64
  • amistre64
try this: 4x^2 + 9y^2 = 72 x - y^2 = -1 (*9) 4x^2 + 9y^2 = 72 9x - 9y^2 = -9 ----------------- 4x^2 +9x = 63 4x^2 =9x -63 = 0 ; solve the quadratic now
amistre64
  • amistre64
4x^2 +9x -63 = 0 x = -9/8 + sqrt(81 -4(4)(63))/8 x = -9/8 - sqrt(81 -4(4)(63))/8
amistre64
  • amistre64
x = -9/8 +- sqrt(1089)/8
amistre64
  • amistre64
x = -9 +- 33 --------- 8
amistre64
  • amistre64
x = 24/8 = 3 x = -42/8 = -21/4 = -5.25
amistre64
  • amistre64
plug these into one of the equations to solve for y
anonymous
  • anonymous
For what it's worth, you were (in my opinion) doing it the hard way (not that it makes much difference): \[x - y^2 = -1 \implies y^2 = x+1\] Which we can then use in the first equation: \[4x^2+9(x+1)=72 \implies ... \]
amistre64
  • amistre64
-72+9 = -63 .... yay!! .. validation ;)
anonymous
  • anonymous
thnx guys
anonymous
  • anonymous
Note when finding all solutions \[y^2 = x+1 \implies y=\pm \sqrt{x+1}\] so it will lead to 4 (x,y) pairs.
amistre64
  • amistre64
yeah, that first bit was definetly going down the wrong path... lol
amistre64
  • amistre64
a parabola joined to an ellipse i think would produce at most 2 real points. right?
amistre64
  • amistre64
nah; 4 is right lol
anonymous
  • anonymous
(Maybe they aren't all real, hehe!)
amistre64
  • amistre64
i saw it wrong there for a moment :)

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