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If the system of equations 2x + 3y = 5, 4x + ky = 10 has infinitely many solutions then k =?
  • a)
    6
  • b)
    4
  • c)
    3
  • d)
    2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the system of equations 2x + 3y = 5, 4x + ky = 10 has infinitely ma...
Given: 
System of equation:
2x + 3y = 5
4x + ky = 10
Concept:
System of equations
a1x + b1y = c1
a2x + b2y = c2
For Infinite solution
Calculation:
From the equations, it can be deduced that
a1 = 2, b1 = 3, c1 = 5
a2 = 4, b2 = k, c2 = 10
For infinite solutions, 2/4 = 3/k
⇒ k = 6
∴ The value of k is 6.
Important Points:
For unique solution

For inconsistent solution
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Community Answer
If the system of equations 2x + 3y = 5, 4x + ky = 10 has infinitely ma...
Given:
The system of equations is:
1) 2x + 3y = 5
2) 4x + ky = 10

To Find:
The value of k if the system of equations has infinitely many solutions.

Solution:
To determine if the system of equations has infinitely many solutions, we need to check if the two equations are dependent or independent.

1. Dependent Equations:
If the two equations are dependent, it means that one equation is a multiple of the other. In this case, there will be infinitely many solutions.

2. Independent Equations:
If the two equations are independent, it means that they intersect at a single point, and there is a unique solution.

Method:
To check if the equations are dependent or independent, we can compare the slopes of the equations.

Equation 1: 2x + 3y = 5
Rewriting it in slope-intercept form:
3y = -2x + 5
y = (-2/3)x + 5/3

Equation 2: 4x + ky = 10
Rewriting it in slope-intercept form:
ky = -4x + 10
y = (-4/k)x + 10/k

Comparing the Slopes:
The slopes of the two equations are -2/3 and -4/k. To have infinitely many solutions, the slopes must be equal.

Therefore, we can equate the slopes:
-2/3 = -4/k

Solving for k:
To solve for k, we can cross-multiply:
-2k = -12

Divide both sides by -2:
k = 6

So, the value of k for which the system of equations has infinitely many solutions is 6 (option A).
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If the system of equations 2x + 3y = 5, 4x + ky = 10 has infinitely many solutions then k =?a)6b)4c)3d)2Correct answer is option 'A'. Can you explain this answer?
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