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if x/a + y/b = a 2 + b 2 and x/a 2 + y/b 2 = a +b, then find x. Solve the equations: 4(2 x-1 ) + 9(3 y-1 ) = 17 and 3(2 x ) – 2(3 y ) = 6

  1. if x/a + y/b = a2 + b2 and x/a2 + y/b2 = a +b, then find x.
  2. Solve the equations: 4(2x-1) + 9(3y-1) = 17 and 3(2x) – 2(3y) = 6

Grade:9

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Please find the answer to your question below
1)Given Equations are
x/a^2 + y/b^2 = 2..........(1)
x/a + y/b = a + b...........(2)
Simplifying equations (1) and (2) by taking lcm we get
b2x+a2y=2a2b2..........(4)
bx+ay=a2b+ab2........(3)
Multiplying equation 3 with b we get
b2x+aby=a2b2+ab3.........(5)
b2x+a2y=2a2b2............(6)
subtracting 5 from 6 we get
(ab-a2)y=ab3-a2b2
a(b-a)y=ab2(b-a)
After cancelling a(b-a) on both sides we get y=b2
substituting y=b2in x/a + y/b = a + b we get x=a2
2)Let4(2x-1) + 9(3y-1) = 17......(1)and 3(2x) – 2(3y) = 6.......(2)
(2x-1+2)+(3y-1+2)=17
(2x+1)+(3y+1)=17
2(2x)+3(3y)=17........(3) and from 2 we have 3(2x)-2(3y)=6
Multiplying eqn 3 by 3 and eqn 2 by 2 we get
6(2x)+9(3y)=51
6(2x)-4(3y)=12
subtracting above 2 equations we get
13(3y)=39 so 3y=31So y=1
Substituting y=1 in 3(2x)-2(3)=6
3(2x)=12 So 2x=4=22 so x=2

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