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# Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev

## Class 10 : Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev

The document Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev is a part of the Class 10 Course Class 10 Mathematics by VP Classes.
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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‡’

Q2. Find the value of k so that the point (3, k) lies on the line represented by x - 5y = 5.
Sol. Substituting (3, k) in x - 5y = 5, we have:
3 - 5k = 5
â‡’ - 5k = 5 - 3 = 2
â‡’
Q3. Determine the value of k for which
kx + 3y = k - 3
12x + ky = k represent coincident lines.
Sol. âˆµ For coincident lines,

âˆ´
â‡’
= 36 â‡’ k = 6
Also
â‡’ 6k = k2 â‡’ k = 6

Q4. If the system of linear equations,
3x + 2y - 4 = 0
px - y - 3 = 0 represents intersecting lines, then find p.
Sol.  a1 = 3, b= 2, c= - 4
a2 = p, b2 = - 1, c2 = - 3
For intersecting lines [i.e., having a unique solution]:

â‡’

Q5. If (a + b) x + (2a - b) y = 21 and 2x + 3y = 7 has infinitely many solutions, then what is â€˜aâ€™ and â€˜bâ€™?
Sol. Here A1 = (a + b), B1 = (2a - b),
C1 = - 21
A2 = 2, B2 = 3, C2 = - 7
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

Q6. Write the relation between the coefficients for which the pair ax + by = c, lx + my = x has a unique solution.
Sol. A1 = a, B1 = b, C1 = c
A2 = l, B2 = m, C2 = n
For a unique solution,

i.e.,

Q7. Check if the pair of linear equations 3x + 6 = 10y and 2x - 15y + 3 = 0 is consistent or not?
Sol. Here, a= 3, b1 = - 10, c1 = 6
a2 = 2, b2 = - 15, c2 = 3
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, a1 = 2, b1 = 2, c1 = 2
a2 = 4, b2 = k, c2 = 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:
=

2 (k - 1) x + y = 1
Sol. We have
=
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., k2 = 36 and 3k â‰  k2 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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