1) x+y=10 2) 2x+y=8 3) x+y=8
x-y=2 x+5= 5 x-y=6
-> solve these graphically.
Answers
Step-by-step explanation:
Given :-
i) x+y = 10 ; x-y = 2
ii) 2x+y = 8 ; x+y = 5
iii) x+y = 8 ; x-y = 6
To find :-
Solve the pair of linear equations graphically ?
Solution :-
i) Given pair of linear equations are x+y = 10
=> x+y-10 = 0
On comparing with a1x + b1y + c1 = 0
a1 = 1
b1 = 1
c1 = -10
and x-y = 2
=> x-y-2 = 0
On comparing with a2x + b2y + c2 = 0
a2 = 1
b2 = -1
c2 = -2
a1/a2 = 1/1 = 1
b1/b2 = 1/-1 = -1
c1/c2 = -10/-2 = 5
we have,
a1/a2 ≠ b1/b2 ≠ c1/c2
Given lines are Consistent and independent or intersecting lines with a unique solution .
Graph :-
The given lines are intersecting lines .
(See the attachment)
ii)Given pair of linear equations are 2x+y = 8
=> 2x+y-8 = 0
On comparing with a1x + b1y + c1 = 0
a1 = 2
b1 = 1
c1 = -8
and x+y = 5
=> x+y-5 = 0
On comparing with a2x + b2y + c2 = 0
a2 = 1
b2 = 1
c2 = -5
a1/a2 = 2/1 = 2
b1/b2 = 1/1 = 1
c1/c2 = -8/-5 = 8/5
we have,
a1/a2 ≠ b1/b2 ≠ c1/c2
Given lines are Consistent and independent or intersecting lines with a unique solution .
(See the attachment)
Graph :-
The given lines are intersecting lines .
iii) Given pair of linear equations are x+y = 8
=> x+y-8 = 0
On comparing with a1x + b1y + c1 = 0
a1 = 1
b1 = 1
c1 = -8
and x-y = 6
=> x-y-6 = 0
On comparing with a2x + b2y + c2 = 0
a2 = 1
b2 = -1
c2 = -6
a1/a2 = 1/1 = 1
b1/b2 = 1/-1 = -1
c1/c2 = -8/-6 = 4/3
we have,
a1/a2 ≠ b1/b2 ≠ c1/c2
Given lines are Consistent and independent with a unique solution .
Graph :-
The given lines are intersecting lines .
(See the attachment)
Answer:-
i) The solution is (6,4)
ii) The solution is (3,2)
iii) The solution is (7,1)
