Question

If am not equal bl, then the system of equations ax+by=K lx+my=n​

Answer 1

Step-by-step explanation:

Given :-

ax+by=K

lx+my=n

am ≠ bl

To find :-

What type of the system of equations are ?

Solution :-

Given pair of linear equations in two variables:

ax+by=K

=> ax +by - K = 0

On Comparing this with a1x+b1y+c1=0 then

a1 = a

b1 = b

c1 = -K

lx+my=n

=> lx+my-n = 0

On Comparing this with a2x+b2y+c2 = 0

a2 = l

b2 = m

c2=-n

Now,

a1/a2 = a/l

b1/b2 = b/m

c1/c2 = -K/n

now

checking

If a1/a2 = b1/b2

a/l = b/m

=> am = bl

But given that

al ≠bm

So

a1/a2 ≠b1/b2

So they are Consistent and Independent lines.

Answer:-

The pair of linear equations in two variables are consistent and independent lines or Parallel lines with a unique solution.

Used formulae:-

If a1x+b1y+c1= 0 and a2x+b2y+c2 = 0 are the system of equations then

• If a1/a2 ≠b1/b2≠c1/c2 they are consistent and independent lines or intersecting lines with a unique solution.

• If a1/a2 = b1/b2 = c1/c2 they are consistent and dependent lines or Coincident lines with infinitely number of many solutions.

• If a1/a2 = b1/b2≠c1/c2 they are inconsistent lines or Parallel lines with no solution.