Question

Is the system of linear equation2x+ 3y- 9=0and 4x + 6y -18 =0 is consistent justify your answer

Answer 1

2x+3y-9=0.......(i)
4x+6y-18=0
2(2x+3y-9)=0
2x+3y-9=0......(ii)

Therefore,
Equation (i) and Equation (ii) are same thus,the system of linear inequation is consistently justified

Answer 2

2x+ 3y- 9=0                           ...(i)

4x + 6y -18 =0                        ...(ii)

Taking 2 common from (ii):

2(2x+3y- 9=0)=0          

⇒ 2x+3y- 9=0                        ...(iii)

So, from (i) and (iii):

a1=2 ; b1= 3 ; c1= -9                   and;

a2=2 ; b2= 3 ; c2= -9

So, it is observed that:-

a1/a2 = b1/b2 = c1/c2

Which is the case for coincident lines (infinitely many solutions)

and also consistent equations.

So, the given pair of equations is consistent.

Hope this helps.