Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution): $3a–5b=20$ $6a–10b=– 40$

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Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution): $3a-5b=20$ $6a-10b=- 40$

Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution): $3a-5b=20$ $6a-10b=- 40$

Given,

$3a-5b=20$ ……. (i)

$6a-10b=-40$ ……. (ii)

From equation (i),

⇒ $b=(3a-20)/5$

When $a=5$ , we have $b=(3(5)-20)/5=-1$

When $a=0$ , we have $b=(3(0)-20)/5=-4$

Thus, we have the following table giving points on the line $3a-5b=20$ .

a	$5$	$0$
b	$-1$	$-4$

From equation (ii),

Solve for b:

⇒ $b=(6a+40)/10$

So, when $a=0$

$b=(6(0)+40)/10=4$

And, when $a=-5$

⇒ $b=(6(-5)+40)/10=1$

Thus, we have the following table giving points on the line $6a-10b=-40$

a	$0$	$-5$
b	$4$	$1$

Graph of the equations (i) and (ii) is given below:

From graph it is clear that, there is no common point between these two lines. Hence, the given systems of equations is in-consistent.

i

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