Question

the roots of equation ax+by+5=0 and bx-ay-12=0 are (2,-3) then find the value of a and b​

Answer 1

Solution

SolutionGiven:-

• Equation are, ax + by = -5 _____(1) , bx - ay = 0_____(2)
• roots of this Equation, ( 2 , -3)

Find:-

• Value ofa & b

Explanation:-

We know ,

(2,-3) roots of both Equation , that's mean these value satisfied of both Equation , for x = 2 & y = -3.

Case 1.

• Keep x. =2 & y = -3 in equ(1)

==> 2a - 3b =-5____________(3)

Case 2.

• keep, x = 2 & y = -3 in equ(2)

==> 2b + 3a = 0

or,

==> 3a + 2b = 0 __________(4)

Multiply by 2 in equ(4) & 3 in equ(3)

• 6a- 9b = -15
• 6a + 4b = 0

____________________(Sub. both)

==> -9b - 4b = -15

==> -13b = -15

==> b = 15/13

Keep value of b in above.

==> 6a - 4 × 15/13= -15

==> 6a = -15 + 60/13

==> 6a = (-195 + 60)/13

==> 6a = - 135/13

==> a = -135/78

==> a = - 45/26

Hence

• Value of a = -45/26
• Value of b = 15/13

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