Question

2x-3y=8

4x-6y=9

the following pair of linear equation is consistent or inconsistent?

Answer 1

given,

2x-3y -8=0

4x-6y-9=0.

a1 =2 ,b1=-3. , c1=-8
a2=4. ,b2=-6. , c2=-9

a1/a2=b1/b2 ≠c1/c2



hence following linear equation is inconsistent.

hope it helps :)

Answer 2

Given : Pair of linear equation $2x- 3y=8 \text { and } 4x-6y=9$

To find: Check consistent or inconsistent

Step-by-step explanation:

Now

$a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$

As we know the pair of equation lines are consistent if there exits at least one solution

So

$2x- 3y=8 \text { and } 4x-6y=9$ we have

$a_1=2, a_2=4,b_1=-3,b_4=-6,c_1=-8,c_2=-9$

$\dfrac{a_1}{a_2} =\dfrac{2}{4} =\dfrac{1}{2}\\\\ \dfrac{b_1}{b_2}=\dfrac{-4}{-6} =\dfrac{2}{3} \\\\ \dfrac{c_1}{c_2} =\dfrac{-8}{-9}=\dfrac{8}{9}$

As it can be seen

$\dfrac{a_1}{a_2}\neq \dfrac{b_1}{b_2}$

Therefore there exists a unique solution

Hence, given pair of equations are consistent