Question

check whether the pair of equations x+4y-6=0and 2x+7y-7=0 are consistent​

Answer 1

We have, x- 2y=5 and 2x+3y=10

Now, x- 2y=5

= x = 5+2y

When y=0 then, x= 5

When y=-2 then, x=1

Thus, we have the following table giving points on the line x-2y =5

X 5 -1

Y 0 -2

Now , 2x+3y=10 =x= 10−3y2

When y=0, then x=5

When y=2 , then x= 2Thus, we have the following table giving poi

mark me pleae

Answer 2

Answer:

Yes.The given lines are consistent.

Step-by-step explanation:

x + 4y - 6  = 0----- ( 1 )     x 2...............   2x + 8y - 12  = 0

2x + 7y - 7 = 0-----( 2  )  x 1 ................   2x + 7y - 7 = 0

                                                        ( - )   ( - )   ( + )

y - 5 = 0

y = 5

Substituting   y=5 in ...(1)   x + 4y - 6  =0

x + 4 ( 5 ) - 6  = 0

x + 20 - 6 = 0

x + 14  = 0

x = -14

OR

Algebraically,

if a1 / a2 ≠ b1 / b2 then, the pair of  linear equations is consistent.

Consider two lines having equation to be-

x + 4y - 6  = 0

2x + 7y - 7 = 0  comparing with

a1x+b1y+c1 = 0 and  

a2x+b2y+c2 = 0  

a1 / a2 ≠ b1 / b2

1 / 2 ≠4 / 7

So the given lines are consistent.