# If the same values of x and y satisfy the following equations; find the value of p: 3x + 7y + 5 =0 4x - 3y - 8 = 0 px + y - 1 = 0

2
by Chottu1501

2014-10-23T17:51:30+05:30
x            y            1
7           5            3           7
-3         -8            4           -3
x /-56+15 = y/20+24  = 1/-9-28
x/-41        = y/44        =  1/-37
x = -41/-37 , y = 44/-37
x = 41/37   , y = -44/37
Substitute x,y values in px + y -1 = 0
p(41/37) + (-44/37) - 1 = 0
(41p-44-37)/37 = 0
41p-81       = 0
41p          = 81
p           = 81/41

2014-10-23T18:09:00+05:30

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First find the values of x and y which satisfy the first two equations.
3x + 7y + 5 =0    ---------(1)
4x - 3y - 8 = 0     ----------(2)

multiply eqn(1) with 4 and eqn(2) with 3
4×(3x + 7y + 5) =4×0
⇒12x + 28y + 20 = 0   -------------(3)
3×(4x - 3y - 8) = 3×0
⇒ 12x -9y - 24 = 0       -------------(4)

subtract eqn(4) from eqn(3), we get
12x + 28y + 20 = 0
12x -  9y  - 24 = 0
-     +       +
37y + 44= 0

⇒ y =

putting y=(-44/37) in equation (1), we get

So x=41/37 and y=(-44/37)