Question

Solve for x and y . 3x - 4y = 1 and 2x - 8/3y = -5

Answer 1

Step-by-step explanation:

Given :-

3x - 4y = 1

and 2x - 8/3y = -5

To find :-

Solve for x and y ?

Solution :-

Given pair of linear equations in two variables are

3x - 4y = 1

=> 3x -4y -1 = 0---------(1)

On Comparing this with a1x+b1y+c1 = 0

a1 = 3

b1 = -4

c1 = -1

and 2x -8/3 y = -5

=> (6x-8y)/3 = -5

=> 6x -8y = -5×3

=> 6x -8y = -15

=> 6x -8y +15 = 0-------(2)

On Comparing this with a2x+b2y+c2 = 0

a2 = 6

b2 = -8

c2 = 15

a1/a2 = 3/6 = 1/2

b1/b2 = -4/-8 = 1/2

c1/c2 = -1/15

a1/a2 = b1/b2 ≠ c1/c2

So , Given pair of linear equations are Inconsistent or Parallel lines.

They have no solution.

Answer:-

The pair of linear equations in two variables have no solution.

Used formulae:-

a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are pair of linear equations in two variables,

• If a1/a2 ≠b1/b2 then they are consistent and independent lines or Intersecting lines with one solution.

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

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