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**Very Short Answer Type Questions**

**Q1. Find the value of k so that graphs of****2x - ky = 9****6x - 9y = 18 will be parallel.Sol.**For graph of equations of system of linear equations to be parallel.

âˆ´

â‡’

3 - 5k = 5

â‡’ - 5k = 5 - 3 = 2

â‡’

âˆ´

â‡’

= 36 â‡’ k = 6

Also

â‡’ 6k = k

a

For intersecting lines [i.e., having a unique solution]:

â‡’

C

A

For infinite number of roots,

â‡’

âˆ´

â‡’ a = 15/3 = 5

a + b =6 â‡’ b = 6 âˆ’ 5 = 1

Thus, a = 5 and b = - 1

A

For a unique solution,

i.e.,

a

For the given pair of linear equations to be consistent,

â‡’

â‡’ which is true.

âˆ´The given system of linear equations is consistent.**Q8. For what value of k, ****2x + 2y + 2 = 0 ****4x + ky + 8 = 0 will have unique solution.****Sol. **Here, a_{1} = 2, b_{1} = 2, c_{1} = 2

a_{2} = 4, b_{2} = k, c_{2} = 8

For the given system of linear equations to have a unique solution.

âˆ´ **Q9. Find the value of k for which the following system represents parallel lines: = **

=

and 2 (k - 1) x + y = 1

for parallel lines,

â‡’

â‡’

â‡’ 3= âˆ’ 2 (k âˆ’ 1)

â‡’ 3= âˆ’ 2k + 2

â‡’ 3 âˆ’ 2= âˆ’ 2k

â‡’ 1= âˆ’ 2k

â‡’ **Q10. What is the point of intersection of the line 3x + 7y = 14 and the y-axis****Sol. **âˆµ For the point of intersection of a line and the y-axis, we put x = 0.

âˆ´ 3x + 7y = 14

â‡’ 3 (0) + 7y = 14

â‡’ 7y = 14 â‡’ y = 2

âˆ´ The point is (0, 2).**Q11. For what value of â€˜aâ€™ does the following pair of linear equations have infinitely many solutions?****4x - 3y - (a - 2) = 0, 8x - 6y - a = 0****Sol.** We have:

4x - 3y - (a - 2) = 0

8x - 6y - a = 0

For infinitely many solutions, we have:

â‡’

â‡’

â‡’

â‡’ 2a âˆ’ 4= a

â‡’ a = 4**Q12. Find the number of solutions of the following pair of linear equations:****x + 2y - 8 = 0****2x + 4y = 16****Sol.**We have:

x + 2y - 8 = 0

2x + 4y - 16 = 0

Here,

âˆ´ The given system of equations has an infinite number of solutions.**Q13. Find the value (s) of â€˜kâ€™ for which the system of linear equations has no solutions.****kx + 3y = k - 2****12x + ky = k **

**Sol.**The given pair of linear equations are:

kx + 3y = k - 2 ...(1)

12x + ky = k ...(2)

For no solution of (1) and (2), we must have

i.e.,

â‡’

i.e., k_{2} = 36 and 3k â‰ k_{2} âˆ’ 2k

i.e., k = Â± 6 and 3 â‰ k âˆ’ 2

or k = Â± 6 and k â‰ 5 â‡’ k = Â± 6**Q14. Write whether the following pair of linear equations is consistent or not:****x + y = 14****x - y = 4 ****Sol.** Here,

Since, for a consistent pair of linear equations, , which is true for the given system [âˆµ 1 â‰ (- 1)]

Thus, it is a consistent pair of linear equations.**Q15. Find the value of k so that the following system of equations has no solution:****3x - y - 5 = 0****6x - 2y - k = 0****Sol. **We have:

Here,

For no solution,

or

â‡’ **Q16. For what value of â€˜aâ€™, the point (3, a) lies on the line represented by 2x - 3y = 5?****Sol.** Since, (3, a) lies on the equation

2x - 3y = 5

âˆ´ (3, a) must satisfy this equation.

â‡’ 2 (3) - 3 (a) = 5

â‡’6 - 3a = 5

â‡’ - 3a = 5 - 6 = - 1

â‡’

Thus the required value of a is 1/3.

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