Question

For what value of k the pair of linear equation has unique solution 2x + 3y=5 , 3x - ky=2​

Answer 1

Step-by-step explanation:

Given:-

2x + 3y=5 , 3x - ky=2

To find:-

For what value of k the pair of linear equation has unique solution 2x + 3y=5 , 3x - ky=2

Solution:-

Given pair of linear equations in two variables are

2X+3Y = 5

=>2X +3Y-5 = 0

a1 = 2

b1 = 3

c1 = -5

and 3X-KY =2

=>3X -KY -2 = 0

a2 = 3

b2 = -K

c2 = -2

Given that the equations has an unique solution

We know that a1/a2≠b1/b2 then the equations has only one solution

=>a1/a2≠b1/b2

=>2/3 ≠3/-K

On applying cross multiplication then

=> -2K ≠ 9

=>K ≠9/-2

=>K ≠ -9/2

Answer:-

The value of k is not equal to -9/2 then the pair of linear equations has unique solution.

Used formulae:-

• a1x+b1y +c1 =0 and a2x +b2y+ c2 =0 are the pair of linear equations then
• If a1/a2≠b1/b2 then they have a unique solution and they are consistent and independent lines.
• If a1/a2=b1/b2 then they have no solution and they are inconsistent lines.
• If a1/a2=b1/b2=c1/c2 then they have infinitely number of many solutions and they are consistent and dependent lines.