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

Class 10 Mathematics by VP Classes

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.
All you need of Class 10 at this link: Class 10

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

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
⇒ - 5k = 5 - 3 = 2
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Q3. Determine the value of k for which
kx + 3y = k - 3
12x + ky = k represent coincident lines.
Sol. ∵ For coincident lines,
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
= 36 ⇒ k = 6
Also Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
⇒ 6k = k2 ⇒ 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]:
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev

Q5. If (a + b) x + (2a - b) y = 21 and 2x + 3y = 7 has infinitely many solutions, then what is ‘a’ and ‘b’?
Sol. Here A1 = (a + b), B1 = (2a - b),
C1 = - 21
A2 = 2, B2 = 3, C2 = - 7
For infinite number of roots,
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
⇒ a = 15/3 = 5
a + b =6 ⇒ b = 6 − 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,
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
i.e., Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev

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

Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev which is true.
∴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.
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev

Q9. Find the value of k for which the following system represents parallel lines:
 = 
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
2 (k - 1) x + y = 1
Sol. We have
= Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
and 2 (k - 1) x + y = 1
for parallel lines,
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
⇒ 3= − 2 (k − 1)
⇒ 3= − 2k + 2 

⇒ 3 − 2= − 2k
⇒ 1= − 2k
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev

Q10. What is the point of intersection of the line 3x + 7y = 14 and the y-axis
Sol. ∵ For the point of intersection of a line and the y-axis, we put x = 0.
∴ 3x + 7y  = 14
⇒ 3 (0) + 7y  = 14
⇒ 7y = 14  ⇒ y = 2
∴ The point is (0, 2).

Q11. For what value of ‘a’ 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:
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
⇒ 2a − 4= a
⇒ 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,
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
∴ The given system of equations has an infinite number of solutions.

Q13. Find the value (s) of ‘k’ 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
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
i.e., Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
i.e., k2 = 36 and 3k ≠ k2 − 2k
i.e., k = ± 6 and 3 ≠ k − 2
or k = ± 6 and k ≠ 5 ⇒ k = ± 6

Q14. Write whether the following pair of linear equations is consistent or not:
x + y = 14
x - y =  4  
Sol. Here,   Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Since, for a consistent pair of linear equations, Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev , which is true for the given system [∵ 1 ≠ (- 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, Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
For no solution, Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
or Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev

Q16. For what value of ‘a’, the point (3, a) lies on the line represented by 2x - 3y = 5?
Sol. Since, (3, a) lies on the equation
2x - 3y = 5
∴ (3, a) must satisfy this equation.
⇒ 2 (3) - 3 (a) = 5
⇒6 - 3a = 5
⇒ - 3a = 5 - 6 = - 1
⇒  Additional Questions Solution - Pair of Linear Equations in Two Variable Class 10 Notes | EduRev
Thus the required value of a is 1/3.

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