find the ratio of (4x - 5y) and (5x + 2y) , if (2x - y) : (2x + 4y) = 1:4 Option a> 3/26 b> 7/17 c> 1/26 d> 21/7
Answers
Answer:
Solution:
(i) x + y = 5; x + y -5=0
2 x + 2 y = 10 2 x + 2 y - 10 =0
on comparing with ax+by+c+0
a1= 1 , b1=1, c1= -5
a2=2, b2=2, c2= - 10
a1/a2 = 1/2
b1/b2 = 1/2 &
c1/c2 = 5/10 = 1/2
Hence, a1/a2 = b1/b2 = c1/c2
Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions. Hence, the pair of linear equations is consistent.
Now we need to solve it graphically
[ graph is in the attachment]
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(ii) x – y = 8, x -y -8=0
3x – 3y = 16, 3 x-3 y-16=0
on comparing with ax+by+c+0
a1= 1 , b1= -1, c1= -8
a2=3, b2=-3, c2= - 16
a1/a2 = 1/3
b1/b2 = -1/-3 = 1/3
c1/c2 = 8/16 = 1/2
Hence, a1/a2 = b1/b2 ≠ c1/c2
Therefore, these linear equations are parallel to each other and thus have no possible solution. Hence, the pair of linear equations is inconsistent.
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(iii) 2x + y – 6 = 0,
4x – 2y – 4 = 0
on comparing with ax+by+c+0
a1= 2 , b1= 1, c1= -6
a2=4, b2=-2, c2= -4
a1/a2 = 2/4 = 1/2
b1/b2 = -1/2 and
c1/c2 = -6/-4 = 3/2
Hence, a1/a2 ≠ b1/b2
Therefore, these linear equations are intersecting each other at one point and thus have only one possible solution. Hence, the pair of linear equations is consistent.
Now we need to solve it graphically.
[ graph is in the attachment]
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(iv) 2x – 2y – 2 = 0,
4x – 4y – 5 = 0
on comparing with ax+by+c+0
a1= 2 , b1= -2, c1= -2
a2=4, b2=-4, c2= -5
a1/a2 = 2/4 = 1/2
b1/b2 = -2/-4 = 1/2
c1/c2 = 2/5
Hence, a1/a2 = b1/b2 ≠ c1/c2
Therefore, these linear equations are parallel to each other and thus, have no possible solution.
Hence, the pair of linear equations is inconsistent.
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Hope this will help you....