Question

Show that the pair of equation 2y = 4x-6,2x=y+3has
on finite Solutions​

Answer 1

Answer:

To prove:

2y = 4x-6, 2x=y+3 has  on finite Solutions​

0= 4x-2y-6  or

4x-2y-6 =0            

2(2x-y-3) = 0  

(2x-y-3) = 0/2        

2x-y-3 = 0              .......................... (1)                and

2x=y+3

2x-y-3= 0               .......................... (2)

from (1) & (2),

a1= 2, b1= -1,  c1= -3

a2= 2, b2= -1,  c2= -3

Now,

comparing with a1/a2,  b1/b2  and  c1/c2,

a1/a2= b1/b2 = c1/c2       [ Many solutions ]

the pair of equations have infinite number of solutions as they coincide.

And when the lines coincide, all the points will be on the same line as far as they go.

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