Question

The pair of linear equations in two variables 2x+3y=4,x-2y=3 are what to each other​

Answer 1

Answer:

they would have a relation on solving and substitution of one variable in any eq. you want

Answer 2

Question :- The pair of linear equations in two variables 2x+3y = 4, x - 2y = 3 are what to each other ?

Concept :-

• A linear equation in two variables represents a straight line in 2D Cartesian plane .

• If we consider two linear equations in two variables, say :-

➻ a1x + b1y + c1 = 0

➻ a2x + b2y + c2 = 0

Then :-

✪ Both the straight lines will coincide if :-

a1/a2 = b1/b2 = c1/c2

➻ In this case , the system will have infinitely many solutions.

➻ If a consistent system has an infinite number of solutions, it is dependent and consistent.

✪ Both the straight lines will be parallel if :-

a1/a2 = b1/b2 ≠ c1/c2.

➻ In this case , the system will have no solution.

➻ If a system has no solution, it is said to be inconsistent.

✪ Both the straight lines will intersect if :-

a1/a2 ≠ b1/b2.

➻ In this case , the system will have an unique solution.

➻ If a system has at least one solution, it is said to be consistent..

____________________

Solution :-

comparing both given Equations 2x+3y= 4, x-2y = 3 or,

→ 2x + 3y - 4 = 0

→ x - 2y - 3 = 0

with

→ a1x + b1y + c1 = 0

→ a2x + b2y + c2 = 0

we get :-

• a1 = 2
• a2 = 1
• b1 = 3
• b2 = (-2)
• c1 = (-4)
• c2 = (-3) .

Now putting values we get,

→ a1/a2 = 2/1

and,

→ b1/b2 = 3/(-2) = (-3/2) .

since,

→ (2/1) ≠ (-3/2)

Therefore,

→ a1/a2 ≠ b1/b2.

Hence, These linear equations intersect each other at one point and therefore have only one possible solution.