The following system of equations is given: 1. 5x + 2y = 10 .(i) 2. 10x + 4y = 20 .(ii) Multiply equation (i) by 2: (2 × 5x) + (2 × 2y) = 2 × 10 ⇒ 10x + 4y = 20 .(iii) Equation (iii) is identical to equation (ii), i.e., both equations represent the same line. Because both equations are equal, the syRead more
The following system of equations is given:
1. 5x + 2y = 10 .(i)
2. 10x + 4y = 20 .(ii)
The system of equations given is: 1. 2x + 3y = 6 .(i) 2. 4x + 6y = 12 .(ii) Multiply equation (i) by 2: (2 × 2x) + (2 × 3y) = 2 × 6 ⇒ 4x + 6y = 12 .(iii) Equation (iii) is identical to equation (ii), i.e., both equations are the same line. Because both equations are equal, the system possesses infinRead more
The system of equations given is:
1. 2x + 3y = 6 .(i)
2. 4x + 6y = 12 .(ii)
Multiply equation (i) by 2:
(2 × 2x) + (2 × 3y) = 2 × 6
⇒ 4x + 6y = 12 .(iii)
Equation (iii) is identical to equation (ii), i.e., both equations are the same line.
Because both equations are equal, the system possesses infinitely many solutions.
If a set of linear equations is consistent and dependent, it implies both equations describe the same line. Graphically, this implies the two lines coincide with one another and completely overlap. Click here for more: https://www.tiwariacademy.in/ncert-solutions/class-10/maths/
If a set of linear equations is consistent and dependent, it implies both equations describe the same line.
Graphically, this implies the two lines coincide with one another and completely overlap.
The system of equations given is: 1. x – y = 2 .(i) 2. x + y = 4 .(ii) Add (i) and (ii): (x – y) + (x + y) = 2 + 4 ⇒ 2x = 6 ⇒ x = 3 Putting x = 3 in (i): 3 – y = 2 ⇒ y = 1
The system of equations given is:
1. x – y = 2 .(i)
2. x + y = 4 .(ii)
Step 1: Understanding Unique Solution Conditions • A system of two linear equations has a unique solution when the equations are linearly independent. • Linear independence means the lines represented by these equations are not parallel. Step 2: Mathematical Representation Given equations: 1. 3x + 4Read more
Step 1: Understanding Unique Solution Conditions
• A system of two linear equations has a unique solution when the equations are linearly independent.
• Linear independence means the lines represented by these equations are not parallel.
The system of equations 5x + 2y = 10 and 10x + 4y = 20 is:
The following system of equations is given: 1. 5x + 2y = 10 .(i) 2. 10x + 4y = 20 .(ii) Multiply equation (i) by 2: (2 × 5x) + (2 × 2y) = 2 × 10 ⇒ 10x + 4y = 20 .(iii) Equation (iii) is identical to equation (ii), i.e., both equations represent the same line. Because both equations are equal, the syRead more
The following system of equations is given:
1. 5x + 2y = 10 .(i)
2. 10x + 4y = 20 .(ii)
Multiply equation (i) by 2:
(2 × 5x) + (2 × 2y) = 2 × 10
⇒ 10x + 4y = 20 .(iii)
Equation (iii) is identical to equation (ii), i.e., both equations represent the same line.
Because both equations are equal, the system has an infinite number of solutions.
Click here for more:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
The number of solutions of the pair of equations 2x + 3y = 6 and 4x + 6y = 12 is:
The system of equations given is: 1. 2x + 3y = 6 .(i) 2. 4x + 6y = 12 .(ii) Multiply equation (i) by 2: (2 × 2x) + (2 × 3y) = 2 × 6 ⇒ 4x + 6y = 12 .(iii) Equation (iii) is identical to equation (ii), i.e., both equations are the same line. Because both equations are equal, the system possesses infinRead more
The system of equations given is:
1. 2x + 3y = 6 .(i)
2. 4x + 6y = 12 .(ii)
Multiply equation (i) by 2:
(2 × 2x) + (2 × 3y) = 2 × 6
⇒ 4x + 6y = 12 .(iii)
Equation (iii) is identical to equation (ii), i.e., both equations are the same line.
Because both equations are equal, the system possesses infinitely many solutions.
Click here for more:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
If a pair of linear equations is consistent and dependent, then its graph will be:
If a set of linear equations is consistent and dependent, it implies both equations describe the same line. Graphically, this implies the two lines coincide with one another and completely overlap. Click here for more: https://www.tiwariacademy.in/ncert-solutions/class-10/maths/
If a set of linear equations is consistent and dependent, it implies both equations describe the same line.
Graphically, this implies the two lines coincide with one another and completely overlap.
Click here for more:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
The solution of the pair of equations x – y = 2 and x + y = 4 is:
The system of equations given is: 1. x – y = 2 .(i) 2. x + y = 4 .(ii) Add (i) and (ii): (x – y) + (x + y) = 2 + 4 ⇒ 2x = 6 ⇒ x = 3 Putting x = 3 in (i): 3 – y = 2 ⇒ y = 1
The system of equations given is:
1. x – y = 2 .(i)
2. x + y = 4 .(ii)
Add (i) and (ii):
(x – y) + (x + y) = 2 + 4
⇒ 2x = 6
⇒ x = 3
Putting x = 3 in (i):
3 – y = 2
See less⇒ y = 1
If 3x + 4y = 10 and 6x + ky = 20 have a unique solution, then the value of k must not be:
Step 1: Understanding Unique Solution Conditions • A system of two linear equations has a unique solution when the equations are linearly independent. • Linear independence means the lines represented by these equations are not parallel. Step 2: Mathematical Representation Given equations: 1. 3x + 4Read more
Step 1: Understanding Unique Solution Conditions
• A system of two linear equations has a unique solution when the equations are linearly independent.
• Linear independence means the lines represented by these equations are not parallel.
Step 2: Mathematical Representation
Given equations:
1. 3x + 4y = 10 (Equation ₁)
2. 6x + ky = 20 (Equation ₂)
Step 3: Condition for Unique Solution
For a unique solution, the coefficient matrix must have a non-zero determinant.
Coefficient matrix = [³⁄₁ ⁴⁄₁]
[⁶⁄₁ ᵏ⁄₁]
Step 4: Determinant Calculation
det = (3 * k) – (4 * 6)
= 3k – 24
Step 5: Uniqueness Condition
For unique solution, det ≠ 0
3k – 24 ≠ 0
3k ≠ 24
k ≠ 8
Step 6: Identifying Impossible k
The condition k = 8 makes the lines parallel, preventing a unique solution.
Click here for more:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/