Question

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Answer 1

Question

Is the system of linear equation 2x + 3y - 9 = 0 and 4x + 6y - 18 = 0 is consistent? Justify your answer

Solution:-

Consistent means:- the system of a pair of linear equations

has infinite number of solution

For infinite numbers solution conditions is

$\to \rm \: \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$

The given system of equation is

2x + 3y - 9 = 0 and

4x + 6y - 18 = 0

These equation are of the form of

$\rm \: a_1x + b_1y + c_1 = 0 \: \: and \: \: a_2x + b_2y + c_2 = 0$

where

$\rm \: a_1 = 2,b_1 = 3 \: \: and \: c_1 = - 9 \: \: \\ \rm \: a_2 = 4,b_2 = 6 \: \: and \: c_2 = - 18$

$\rm \therefore \: \frac{a_1}{a_2} = \frac{2}{4} = \frac{1}{2} , \frac{b_1}{b_2} = \frac{3}{6} = \frac{1}{2 } \: and \: \frac{c_1}{c_2} = \frac{ - 9}{ - 18} = \frac{1}{2}$

Thus

$\rm \: \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$

So ,

the system of linear equation is consistent

More information about consistent and inconsistent

A system of equation

$\rm \: a_1x + b_1y + c_1 = 0 \: \: and \: \: a_2x + b_2y + c_2 = 0$

is said to consistent if it has at least one solution. on the other hand the above system is said to be inconsistent if has no solution at all

Answer 2

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