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1. Write the condition for which the pair of equations ax + 2y =7 and 3x + by =16 represent parallel line?
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1. Write the condition for which the pair of equations ax + 2y =7 and ...
Condition for Parallel Lines:
Same Slopes:
ax + 2y = 7
2y = -ax + 7
y = (-a/2)x + 7/2
3x + by = 16
by = -3x + 16
y = (-3/b)x + 16/b
a/b = 6
Different y-Intercepts:
ax + 2y = 7
2y = 7
y = 7/2
3x + by = 16
by = 16
y = 16/b
a ≠ 24
Conclusion:
Two lines are said to be parallel if they never intersect each other. In other words, they have the same slope but different y-intercepts. The condition for which the pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines are:
Same Slopes:
The slopes of the two lines must be equal for them to be parallel. The slope of the first line can be found by rearranging the equation into slope-intercept form:
ax + 2y = 7
2y = -ax + 7
y = (-a/2)x + 7/2
The slope of the first line is -a/2. Similarly, the slope of the second line can be found by rearranging the equation into slope-intercept form:
3x + by = 16
by = -3x + 16
y = (-3/b)x + 16/b
The slope of the second line is -3/b. Therefore, for the two lines to be parallel, -a/2 = -3/b, or:
a/b = 6
Different y-Intercepts:
The two lines must have different y-intercepts for them to be parallel. The y-intercept of the first line can be found by setting x = 0:
ax + 2y = 7
2y = 7
y = 7/2
The y-intercept of the first line is 7/2. Similarly, the y-intercept of the second line can be found by setting x = 0:
3x + by = 16
by = 16
y = 16/b
The y-intercept of the second line is 16/b. Therefore, for the two lines to be parallel, 7/2 ≠ 16/b, or:
a ≠ 24
Conclusion:
Therefore, the condition for which the pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines are a/b = 6 and a ≠ 24.
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1. Write the condition for which the pair of equations ax + 2y =7 and 3x + by =16 represent parallel line?
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1. Write the condition for which the pair of equations ax + 2y =7 and 3x + by =16 represent parallel line? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 1. Write the condition for which the pair of equations ax + 2y =7 and 3x + by =16 represent parallel line? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1. Write the condition for which the pair of equations ax + 2y =7 and 3x + by =16 represent parallel line?.
1. Write the condition for which the pair of equations ax + 2y =7 and 3x + by =16 represent parallel line? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 1. Write the condition for which the pair of equations ax + 2y =7 and 3x + by =16 represent parallel line? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1. Write the condition for which the pair of equations ax + 2y =7 and 3x + by =16 represent parallel line?.
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