Question

check whether given pair of lines is consistent or not 5x-1=2y y=-1/2+5/2x​

Answer 1

5x-2y-1=0

5x-2y+1=0

a1/a2=b1/b2≠c1/c2

So the given lines are incosistent.

Answer 2

The given lines are consistent.

Step-by-step explanation:

Given the pair of lines are:

5x - 1 = 2y

⇒ 5x - 2y - 1 = 0 and

Here, $a_{1} =5,b_{1} =-2 and c_{1} =-1$

$y=-\dfrac{1}{2}+\dfrac{5}{2}x$

⇒ 5x - 2y -1 = 0

Here, $a_{2} =5,b_{2} =-2 and c_{2} =-1$

The condition for lines for consistent.

$\dfrac{a_{1}}{a_{2}} =\dfrac{b_{1}}{b_{2}}=\dfrac{c_{1}}{c_{2}}$

$\dfrac{5}{5} =\dfrac{-2}{-2} =\dfrac{-1}{-1}$

1 = 1 = 1

Hence, the given lines are consistent.