anonymous
  • anonymous
In the system shown below, what are the coordinates of the solution that lies in quadrant I? Write your answer in the form (a,b) without using spaces. x^2-y^2=25 x+y=25
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
First solve one of the equations for one variable. Since both equations have y^2 in them, we'll solve the bottom for y^2: x - y^2 = -5 -y^2 = -x - 5 y^2 = x + 5 Substitute this for y^2 in the first equation: x^2 + (x + 5) = 25 x^2 + x - 20 = 0 Now factor: (x + 5)(x - 4) = 0 x = -5 or x = 4 Since the point is in Quadrant I, we know x has to be positive, so x=4 Now to get y, plug x into one of the equations: x - y^2 = -5 4 - y^2 = -5 -y^2 = -9 y = 3 Your point is (4,3) Hope this helps :-)
anonymous
  • anonymous
\[x^2-y^2=25\] \[(x+y)(x-y)=25\] \[x+y=25\] \[x-y=1\] add to get \[2x=26\] \[x=13\] then solve for y
anonymous
  • anonymous
answer is (13,12) (4,3) does not work because 4 + 3 = 7, not 25

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