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The value of k for which the pair of equations 3x – y = 5 and 6x – 2y = k has infinitely many solutions is:
Step 1: Examining the System of Equations Equation ₁: 3x - y = 5 Equation ₂: 6x - 2y = k Step 2: Infinitely Many Solutions Condition Infinitely many solutions are achieved when the equations define the same line. That is, the equations should be scalar multiples of one another. Step 3: Coefficient CRead more
Step 1: Examining the System of Equations
Equation ₁: 3x – y = 5
Equation ₂: 6x – 2y = k
Step 2: Infinitely Many Solutions Condition
Infinitely many solutions are achieved when the equations define the same line.
That is, the equations should be scalar multiples of one another.
Step 3: Coefficient Comparison
– Equation ₁ coefficients:
– x coefficient: 3
– y coefficient: -1
– Equation ₂ coefficients:
– x coefficient: 6
– y coefficient: -2
Step 4: Checking Proportionality
Notice the proportionality of coefficients:
– x coefficient ratio: 6 ÷ 3 = 2
– y coefficient ratio: -2 ÷ (-1) = 2
Step 5: Constant Term Condition
For an infinite number of solutions, constant terms must also be under the same scaling.
Equations should be equal:
3x – y = 5
6x – 2y = k
Replacing the coefficient scaling:
– If the equations are for the same line, k should be 2 * 5 = 10
Step 6: Checking
If k = 10, the second equation is:
6x – 2y = 10
Divide by 2:
3x – y = 5 (Which is exactly the same as the first equation)
Conclusion:
The value of k for infinitely many solutions is 10.
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In the poem for Anne Gregory, Anne Gregory’s suggestion to dye her hair serves two main purposes. What are these?
Firstly, it aims to gain genuine love by indicating that she can change her hair colour, encouraging young men to love her for her inner self rather than just her yellow hair. Secondly, it seeks to prove a point to the speaker, who doubts that anyone would love her for anything other than her externRead more
Firstly, it aims to gain genuine love by indicating that she can change her hair colour, encouraging young men to love her for her inner self rather than just her yellow hair. Secondly, it seeks to prove a point to the speaker, who doubts that anyone would love her for anything other than her external beauty.
See lessThe 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.
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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.
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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/