Math, asked by nivedita25, 1 year ago

1
3. One equation of a pair of dependent equations is -5x + 2y = 4. The second equation
can be :
a) 10x + 4y + 8 = 0
b) - 10x - 4y + 8 = 0
c) - 10x + 4y = 8
d) 10x - 4y = 8​

Answers

Answered by Anonymous
5

Answer:

The general form for a pair of linear equations in two variables x and y is 

a1x + b1y + c1 = 0 ,

a2x + b2y + c2 = 0 ,

Condition 1: Intersecting Lines

If   a 1 / a 2 ≠  b 1 / b 2  , then the pair of linear equations has a unique solution.

Condition 2: Coincident Lines

If   a 1 / a 2 =  b 1 / b 2 =  c 1 / c 2  ,then the pair of linear equations has infinite solutions.

A pair of linear equations, which has a unique or infinite solutions are said to be a consistent pair of linear equations.

A pair of linear equations, which has  infinite many distinct common solutions are said to be a consistent pair or dependent pair of linear equations.

Condition 3: Parallel Lines

If   a 1/ a 2 =  b 1/  b 2 ≠  c 1 / c 2 , then a pair of linear equations   has no solution.

A pair of linear equations which has no solution is said to be an inconsistent pair of linear equations.

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(i) x – 3y – 3 = 0

3x – 9y – 2 =0

on comparing with ax+by+c+0

a1= 1 ,  b1=-3,  c1= -3

a2=3,    b2=-9,     c2= - 2

a1/a2 = 1/3

b1/b2 = -3/-9 = 1/3 

c1/c2 = -3/-2 = 3/2

a1/a2 = b1/b2 ≠ c1/c2

 

the given sets of lines are parallel to each other. 

Therefore, they will not intersect each other and thus, there will not be any solution for these equations.

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(ii) 2x + y = 5     ,       2x + y- 5  =0

3x +2y = 8  ,              3x +2y -8 =0 

on comparing with ax+by+c+0

a1= 2 ,  b1=1,  c1= -5

a2=3,    b2=2,     c2= -8

a1/a2 = 2/3

b1/b2 = 1/2 

c1/c2 = -5/-8 = 5/8

a1/a2 ≠ b1/b2

Therefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations.

formula for cross multiplication method

x/ b 1 c 2 - b 2 c 1   =  y/ c 1 a 2 - c 2 a 1  = 1/a 1 b 2 - a 2 b 1

x / (1)(-8) - (2)(-5) = y / (-5)(3) - (-8) (2) = 1 / (2) (2) - (3) (1)

x/-8-(-10) = y/-15+16 = 1/4-3

x/2 = y/1 = 1/1

Now take  x/2 =1/1   & y/1 = 1/1

∴ x = 2, y = 1.

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(iii) 3x – 5y = 20 ,           3x – 5y - 20  =0    

6x – 10y = 40 ,                       6x -10y -40 =0

on comparing with ax+by+c+0

a1= 3,  b1=-5,  c1= -20

a2=6,    b2=10,     c2= -40

a1/a2 = 3/6 = 1/2

b1/b2 = -5/-10 = 1/2 

c1/c2 = -20/-40 = 1/2

a1/a2 = b1/b2 = c1/c2

Therefore, the given sets of lines will be overlapping each other i.e., the lines will be coincident to each other and thus, there are infinite many solutions .

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(iv) x – 3y – 7 = 0

3x – 3y – 15= 0

on comparing with ax+by+c+0

a1= 1 ,  b1=-3,  c1= -7

a2=3,    b2=-3,     c2= -15

a1/a2 = 1/3

b1/b2 = -3/-3 = 1 

c1/c2 = -7/-15 = 7/15

a1/a2 ≠ b1/b2

Therefore, they will intersect each other at a unique point and thus, there will be a unique solution 

formula for cross multiplication method

x/ b 1 c 2 - b 2 c 1   =  y/ c 1 a 2 - c 2 a 1  = 1/a 1 b 2 - a 2 b 1

x / (-3) (-15) - (3)(-7) = y / (-7)(3) - (-15)(1) = 1 / (1)(-3) - (3)(-3)

x/45-(21) = y/-21-(-15) = 1/-3-(-9)

x/24 = y/-6 = 1/6

x/24 = 1/6        &  y/-6 = 1/6

x = 4 and y = -1

∴ x = 4, y = -1.

hope this will help u:)

Answered by varishchoudhary515
2

Answer:

10x+4+8is equal 0

Step-by-step explanation:

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