Very Short Answer Questions: Pair of Linear Equations in Two Variable

# Class 10 Maths Chapter 3 Question Answers - Pair of Linear Equations in Two Variables

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

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

Q3. Determine the value of k for which
kx + 3y = k - 3
12x + ky = k represent coincident lines.
Sol. ∵ For coincident lines,

= 36 ⇒ k = 6
Also
⇒ 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]:

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,

⇒ 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,

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,

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.

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,

⇒ 3= − 2 (k − 1)
⇒ 3= − 2k + 2

⇒ 3 − 2= − 2k
⇒ 1= − 2k

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:

⇒ 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,

∴ 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

i.e.,

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,
Since, for a consistent pair of linear equations,  , 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,

For no solution,
or

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
⇒
Thus the required value of a is 1/3.

The document Class 10 Maths Chapter 3 Question Answers - Pair of Linear Equations in Two Variables is a part of the Class 10 Course Mathematics (Maths) Class 10.
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## Mathematics (Maths) Class 10

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## FAQs on Class 10 Maths Chapter 3 Question Answers - Pair of Linear Equations in Two Variables

 1. What is a pair of linear equations in two variables?
Ans. A pair of linear equations in two variables is a set of two equations that involve two variables, typically denoted by x and y, and are in the form ax + by = c. These equations can be graphed as lines on a coordinate plane and represent the relationship between two variables.
 2. How can we solve a pair of linear equations in two variables?
Ans. There are various methods to solve a pair of linear equations in two variables, including substitution method, elimination method, and graphical method. These methods involve manipulating the equations to eliminate one variable and solve for the other variable.
 3. What is the importance of solving a pair of linear equations in two variables?
Ans. Solving a pair of linear equations in two variables is important as it helps in finding the values of the variables that satisfy both equations simultaneously. This can be useful in various real-life situations, such as determining the intersection point of two lines or finding the solutions to systems of equations.
 4. Can a pair of linear equations in two variables have more than one solution?
Ans. Yes, a pair of linear equations in two variables can have more than one solution. This occurs when the two equations represent the same line or when they are parallel lines. In such cases, the equations have infinitely many solutions as all points on the line(s) satisfy both equations.
 5. How can we determine the consistency of a pair of linear equations in two variables?
Ans. The consistency of a pair of linear equations in two variables can be determined by analyzing the slopes and intercepts of the lines represented by the equations. If the lines intersect at a single point, the equations are consistent and have a unique solution. If the lines are parallel and do not intersect, the equations are inconsistent and have no solution.

## Mathematics (Maths) Class 10

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