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