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For what value of k does the system of...

For what value of k does the system of equations
`" " kx + 2y = 5, 3x - 4y = 10 `
have (i) a unique solution, (ii)no solution ?

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Verified by Experts

The correct Answer is:
(i)` k ne (-3)/(2)` (ii) ` k = (-3)/(2)`
(i) ` (k)/(3) ne ( 2)/(-4) rArr (k ) /(3) ne (-1)/(2) rArr k ne (-3)/(2)`
(ii) `(k)/(3) = ( 2)/(-4) ne (5)/(10) rArr (k)/(3) = (-1)/(2) and (k)/(3) ne 1/2 rArr k = (-3)/2`
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RS AGGARWAL-LINEAR EQUATIONS IN TWO VARIABLES -Exercise 3D
  1. Show that the system of equations. " " 2 x - 3y = ...

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  2. Show that the system of equations " " 6x + 5y = 11, ...

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  3. For what value of k does the system of equations " " kx ...

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  4. For what value of k , will the system of equations x+2y=5,\ \ \ \ 3...

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  5. For what value of k does the system of equations " ...

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  6. For what value of k does the system of linear equations 2x+3y=7 ...

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  7. {:(2x + (k - 2)y = k),(6x + (2k - 1) y = 2k + 5):}

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  8. Find the value of k for which following system of equations have in...

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  9. Find the value of k for infinite solutions: 5x + 2y = 2k, 2 ...

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  10. ( k - 1 ) x - y = 5, (k + 1 ) x + ( 1 - k ) y = ( 3k + 1 )

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  11. {:((k - 3)x + 3y = k),(kx + ky = 12):}

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  12. (a - 1) x + 3y = 2, 6x + (1 - 2b) y =6.

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  13. {:((2a - 1)x + 3y - 5 = 0),(3x + (b - 1) y - 2 = 0):}

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  14. If 2x - 3y = 7 and (a+b)x- (a+b-3)y = 4a + b represent coincident lin...

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  15. Find the values of a and b for which the following system of linear eq...

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  16. 2x + 3y =7, (a + b ) x + ( 2a - b ) y = 21.

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  17. If the system of equations 2x + 3y = 7 and 2ax + (a + b) y = 28 has in...

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  18. 8x + 5y = 9 , kx + 10 y = 15.

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  19. kx + 3y = 3, 12 x + k y = 6.

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  20. 3x - y - 5 = 0 , 6x - 2y + k = 0 ( k ne 0 )

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