Question

is the pair of equations x-3y + 4 = 0 and 7x-21y+28 = 0 consistent? Justify your answer. ​​​

Answer 1

Answer:

This pair of equation is consistent because

Step-by-step explanation:

representing graphically , this equation have concident lines

Answer 2

SOLUTION

TO CHECK

Is the pair of equations x - 3y + 4 = 0 and 7x - 21y + 28 = 0 consistent? Justify your answer.

CONCEPT TO BE IMPLEMENTED

For the given two linear equations

$\displaystyle \sf{ a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0}$

Consistent :

One of the Below two condition is satisfied

1. Unique solution :

$\displaystyle \sf{ \: \frac{a_1}{a_2} \ne \frac{b_1}{b_2} }$

2. Infinite number of solutions :

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

Inconsistent :

NO solution

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \: \frac{c_1}{c_2}}$

EVALUATION

Here the given system of equations are

x - 3y + 4 = 0 and 7x - 21y + 28 = 0

Now Comparing with the equations

$\displaystyle \sf{ a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0}$

We get

$\displaystyle \sf\: a_1 = 1 \: , \: b_1 = - 3 , c_1= 4 \: and \: \: a_2 = 7 \: , \: b_2 = - 21\: , \: \: c_2= 28$

Thus we have

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} = \: \frac{c_1}{c_2}} = \frac{1}{7}$

Hence the given system of equations have infinite number of solutions

Hence the given system of equations are consistent

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