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Which of the following equations represents a line that is parallel to the line represented by 3x + 5y = –3? A. 3x + 5y = 2 B. 6x + 10y = –6 C. –5x + 3y = 2 D. –3x + 5y = –3

User Mceo
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Answer:

Option b

The equation 6x + 10y = -6 represents a line that is parallel to the line 3x + 5y = –3

Solution:

let us consider two equations


a_(1) x_(1) + b_(1) y_(1) + c_(1) = 0


a_(2) x_(2) + b_(2) y_(2) + c_(2) = 0

If two equations are parallel to each other,then the condition is


(a_(1))/(a_(2)) = (b_(1))/(b_(2)) = (c_(1))/(c_(2)) ------------- eqn 1

From question, given that 3x + 5y = –3

Hence we get,
a_(1) = 3, b_(1) = 5 \text { and } c_(1) = -3

Applying equation 1 in the given options,

Case 1:

Consider option 1, given that 3x + 5y = 2

Hence we get,
a_(2) = 3, b_(2) = 5 \text { and } c_(2) = 2

By using equation 1,


(3)/(3) = (5)/(5) \\eq (-3)/(2)

Hence the condition is not satisfied.

Case 2:

Consider option 2, given that 6x + 10y = –6

Hence we get,
a_(2) = 6 \text { and } b_(2) = 10 \text { and } c_(2) = -6

By using equation 1,


(3)/(6) = (5)/(10) = (-3)/(-6)

By simplifying we get,


(1)/(2) = (1)/(2) = (1)/(2)

Hence the condition is satisfied. So, 6x + 10y = –6 represents the line which is parallel to 3x + 5y = –3

Case 3:

Consider option 3, given that -5x + 3y = –2

Hence we get,
a_(2) = -5 \text { and } b_(2) = 3 \text { and } c_(2) = -2

By using equation 1,


(3)/(-5) \\eq (5)/(3) \\eq (-3)/(-2)

Hence the condition is not satisfied.

Case 4:

Consider option 4, given that –3x + 5y = –3

Hence we get
a_(2) = -3 \text { and } b_(2 )= 5 \text { and } c_(2) = -3

By using equation 1,


(3)/(-3) \\eq (5)/(5) \\eq (-3)/(-3)

Hence the condition is not satisfied.

Thus the correct answer is option b

User Cesards
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