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
[tex]a_{1} x_{1} + b_{1} y_{1} + c_{1} = 0[/tex]
[tex]a_{2} x_{2} + b_{2} y_{2} + c_{2} = 0[/tex]
If two equations are parallel to each other,then the condition is
[tex]\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}[/tex] ------------- eqn 1
From question, given that 3x + 5y = –3
Hence we get, [tex]a_{1} = 3, b_{1} = 5 \text { and } c_{1} = -3[/tex]
Applying equation 1 in the given options,
Case 1:
Consider option 1, given that 3x + 5y = 2
Hence we get, [tex]a_{2} = 3, b_{2} = 5 \text { and } c_{2} = 2[/tex]
By using equation 1,
[tex]\frac{3}{3} = \frac{5}{5} \neq \frac{-3}{2}[/tex]
Hence the condition is not satisfied.
Case 2:
Consider option 2, given that 6x + 10y = –6
Hence we get, [tex]a_{2} = 6 \text { and } b_{2} = 10 \text { and } c_{2} = -6[/tex]
By using equation 1,
[tex]\frac{3}{6} = \frac{5}{10} = \frac{-3}{-6}[/tex]
By simplifying we get,
[tex]\frac{1}{2} = \frac{1}{2} = \frac{1}{2}[/tex]
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, [tex]a_{2} = -5 \text { and } b_{2} = 3 \text { and } c_{2} = -2[/tex]
By using equation 1,
[tex]\frac{3}{-5} \neq \frac{5}{3} \neq \frac{-3}{-2}[/tex]
Hence the condition is not satisfied.
Case 4:
Consider option 4, given that –3x + 5y = –3
Hence we get [tex]a_{2} = -3 \text { and } b_{2 }= 5 \text { and } c_{2} = -3[/tex]
By using equation 1,
[tex]\frac{3}{-3} \neq \frac{5}{5} \neq \frac{-3}{-3}[/tex]
Hence the condition is not satisfied.
Thus the correct answer is option b
