If the equations 14x + 8y + 5 = 0 and 21x - ky - 7 = 0 have no solution, then the value of k is:a)12b)-12c)8d)-16Correct answer is option 'B'. Can you explain this answer?

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SAT Exam > SAT Questions > If the equations 14x + 8y + 5 = 0 and 21x - k...

If the equations 14x + 8y + 5 = 0 and 21x - ky - 7 = 0 have no solution, then the value of k is:

a)
12
b)
-12
c)
8
d)
-16

Correct answer is option 'B'. Can you explain this answer?

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Verified Answer

If the equations 14x + 8y + 5 = 0 and 21x - ky - 7 = 0 have no solutio...

⇒ The equations have no solution when their slopes are same

⇒ Slope of equation 1 = - 14/8 = - 7/4

⇒ Slope of equation 2 = 21/k

⇒ So, 21/k = - 7/4

∴ The value of k is - 12.

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Most Upvoted Answer

If the equations 14x + 8y + 5 = 0 and 21x - ky - 7 = 0 have no solutio...

Given:
Equation 1: 14x + 8y + 5 = 0
Equation 2: 21x - ky - 7 = 0

To Find:
The value of k if the equations have no solution.

Explanation:
When two linear equations have no solution, it means that the lines represented by these equations are parallel and never intersect. In other words, the slopes of the lines are equal but the y-intercepts are different.

Step 1: Find the Slopes of the Lines
The slopes of the lines can be found by rearranging the equations in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Equation 1: 14x + 8y + 5 = 0
Rearranging, we get:
8y = -14x - 5
y = (-14/8)x - 5/8
Slope of line 1 = -14/8 = -7/4

Equation 2: 21x - ky - 7 = 0
Rearranging, we get:
ky = 21x - 7
y = (21/k)x - 7/k
Slope of line 2 = 21/k

Step 2: Compare the Slopes
Since the lines are parallel, their slopes must be equal. Therefore, we can set the slopes equal to each other and solve for k.

-7/4 = 21/k

Step 3: Solve for k
To solve for k, we can cross multiply and then isolate k.

-7k = 84
k = -84/-7
k = 12

Conclusion:
The value of k that makes the equations have no solution is 12. Therefore, the correct answer is option B).

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Community Answer

If the equations 14x + 8y + 5 = 0 and 21x - ky - 7 = 0 have no solutio...

⇒ The equations have no solution when their slopes are same

⇒ Slope of equation 1 = - 14/8 = - 7/4

⇒ Slope of equation 2 = 21/k

⇒ So, 21/k = - 7/4

∴ The value of k is - 12.

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