please answer these questions .
Find linear equation for these questions...
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Answers
Step-by-step explanation:
Solutions :-
12)
Given pair of linear equations are :-
2y+4x = 8
=> 4x+2y-8 = 0
=> 2(2x+y-4) = 0
=> 2x+y-4 = 0/2
=> 2x+y-4 = 0
On comparing with a1x+b1y+c1 = 0
a1 = 2, b1 = 1 , c1 = -4
and
3y+6x = 12
=> 6x+3y-12 = 0
=> 3(2x+y-4) = 0
=> 2x+y-4 = 0/3
=> 2x+y-4 = 0
On comparing with a2x+b2y+c2 = 0
a2 = 2 , b2 = 1 , c2 = -4
Now,
a1/a2 = 2/2 = 1
b1/b2 = 1/1 = 1
c1/c2 = -4/-4 = 1
We have,
a1/a2 = b1/b2 = c1/c2
So, Given pair of linear equations in two variables have infinite number of many solutions .
13)
Given pair of linear equations are :-
5x-y = 20 ---------(1)
On comparing with a1x+b1y+c1 = 0
a1 = 5, b1 = -1 , c1 = -20
7x+y = 10 ---------(2)
On comparing with a2x+b2y+c2 = 0
a2 = 7 , b2 = 1 , c2 = -10
a1/a2 = 5/7
b1/b2 = -1/1 = -1
c1/c2 = -20/-10 = 2
We have,
a1/a2 ≠ b1/b2 ≠ c1/c2
So, Given pair of linear equations in two variables have a unique solution.
Now,
On adding (1)&(2) then
5x-y = 20
7x+y = 10
(+)
________
12x +0 = 30
_________
=> 12x = 30
=> x = 30/12
=> x = 5/2
On Substituting the value of x in (1) then
=> 5(5/2)-y = 20
=> (25/2)-y = 20
=> y = (25/2)-20
=> y = (25-40)/2
=> y = -15/2
Therefore , The solution = (5/2, -15/2)
14)
Given pair of linear equations are :-
x+2y= 7 ---------(1)
On comparing with a1x+b1y+c1 = 0
a1 = 1, b1 = 2, c1 = -7
x-y = 1 ---------(2)
On comparing with a2x+b2y+c2 = 0
a2 = 1, b2 = -1 , c2 = -1
a1/a2 = 1/1 = 1
b1/b2 = 2/-1 = -2
c1/c2 = -7/-1 = 7
We have,
a1/a2 ≠ b1/b2 ≠ c1/c2
So, Given pair of linear equations in two variables have a unique solution.
Now,
On Subtracting (2) from (1) then
x+2y = 7
x-y = 1
(-)
________
0 +3y = 6
_________
=> 3y = 6
=> y = 6/3
=> y = 2
On Substituting the value of y in (1) then
=> x-2 = 1
=> x = 1+2
=> x = 3
Therefore , The solution = (3, 2)
15)
Given pair of linear equations are :-
3x+y = 8 ---------(1)
On comparing with a1x+b1y+c1 = 0
a1 = 3, b1 = 1, c1 = 8
5x+y = 10---------(2)
On comparing with a2x+b2y+c2 = 0
a2 = 5, b2 = 1, c2 = -10
a1/a2 = 3/5
b1/b2 = 1/1= 1
c1/c2 = 8/10=4/5
We have,
a1/a2 ≠ b1/b2 ≠ c1/c2
So, Given pair of linear equations in two variables have a unique solution.
Now,
On Subtracting (2) from (1) then
3x+y = 8
5x+y = 10
(-)
________
-2x+0 = -2
_________
=> -2x = -2
=> 2x = 2
=> x = 2/2
=> x = 1
On Substituting the value of x in (1) then
=> 3(1)+y = 8
=> 3+y = 8
=> y = 8-3
=> y = 5
Therefore , The solution = (1,5)
Used Method :-
Method of Elimination
Used formulae:-
If a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are pair of linear equations in two variables then
→ If a1/a2 ≠b1/b2 ≠ c1/c2 then they are Consistent and independent lines or Intersecting lines and they have a unique solution.
→ If a1/a2 = b1/b2 = c1/c2 then they are Consistent and dependent lines or Coincident lines and they have infinitely number of many solutions.
→ If a1/a2 =b1/b2 ≠ c1/c2 then they are Inconsistent lines or Parallel lines lines and they have no solution.