MathematicsSolve the following pair of equations using the substitution method.5y2-x3=8 and y2+5×3=12.

Solve the following pair of equations using the substitution method.


5y2-x3=8 and y2+5x3=12.


  1. A
    x=2, y=7
  2. B
    x=6, y=4
  3. C
    x=7, y=1
  4. D
    x=8, y=3  

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    Solution:

    Given equations are,
    5y2-x3=8 and,
    y2+5x3=12 .
    Let y2=a and x3=b .
    So, the original equations will reduce to,
    5a-b=8... (1) and,
    a+5b=12... (2)
    From (1),b=5a-8 Substituting b=5a-8 in (2),
    we get,
    a+5(5a-8)=12 ⇒ a+25a-40=12 ⇒ 26a=52 ⇒ a=2 So, b=5a-8
    ⇒ b=10-8
    ⇒ b=2 But  y2=a 
    ⇒ y=2a ⇒ y=2(2)
    ⇒ y=4
    ⇒ x3=b 
    ⇒ x=3b ⇒ x=3(2)
    ⇒ x=6
    ⇒ x=6, y=4.
    Hence, the correct option is 2.
     
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