Question

Q) Check whether the following pair of linear equations are consistent or inconsistent.
6x – 4y + 10 = 0; 3x – 2y = –5

If you don't know please don't answer, If anyone gives silly or irrevelent answers I will report them.

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Answer 1

Answer:

consistent

Step-by-step explanation:

6x-4y+10= 0

taking 2 common from equation

2(3x-2y+5) = 0. ........ equation 1

and another equation

3x-2y= -5

3x-2y+5=0........... equation 2

from equation 1and2

We can say that equation are consistent

Answer 2

Answer:

Consistent

Step-by-step explanation:

6x – 4y + 10 = 0 ---- eqn 1

3x – 2y = –5 or

3x – 2y + 5 = 0 ---- eqn 2

A pair of linear equations are consistent only if they intersect at one point or are coincident.

For intersecting lines, a1/a2 ≠ b1/b2 while for coincident lines,

a1/a2 = b1/b2 = c1/c2 where a1&a2 are the coefficients of x,

b1&b2 are the coefficients of y and c1&c2 are the constant term.

For this pair of equations,

a1=6, b1= -4, c1=10

a2=3, b2= -2, c2=5

Here, a1/a2 =6/3=2/1=2

b1/b2= -4/(-2) = 2/1=2

c1/c2= 10/5 = 2/1=2

As a1/a2 = b1/b2 = c1/c2, the lines are coincident and have infinite number of solutions. Hence the given pair is consistent.