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✧ CLASS -9 -MATHS- CHAPTER 4- LINEAR EQUATIONS IN TWO VARIABLES
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Answer:
2)
i) (0,7) (1,5) (-1,9) ( 2,3)
ii) (0,9) (1, 9-π) (2,9-2π) (3, 9-3π)
iii) (0,0) (4,1) (8,2) (12,3)
Step-by-step explanation:
Solutions :-
1.
Option (iii)
Reason :-
Given equation is y = 3x+5
It is a linear equation in two variables
So it has infinitely number of many solutions.
2.
(i)
Given equation is 2x+y = 7
Put x = 0 then
2(0)+y = 7
=> 0+y = 7
=> y = 7
The first solution = (0,7)
Put y = 0 then
2x+0 = 7
=> 2x = 7
=> x = 7/2
The second solution = (7/2,0)
Put x = 1 then
2(1)+y = 7
=> 2+y = 7
=> y = 7-2
=> y = 5
The third solution = (1,5)
Put y= 1 then
2x+1 = 7
=> 2x = 7-1
=> 2x = 6
=> x = 6/2
=> x = 3
The fourth solution = (3,1)
ii)
Given equation is πx+y = 9
Put x = 0 then
π(0)+y = 9
=> 0+y = 9
=> y = 9
The first solution = (0,9)
Put y = 0 then
πx+0 = 9
=> πx = 9
=> x = 9/π
The second solution = (9/π,0)
Put x = 1 then
π(1)+y = 9
=> π+y = 9
=> y = 9-π
The third solution = (1, 9-π)
Put y= 1 then
πx+1 = 9
=> πx = 9-1
=> πx = 8
=> x = 8/π
The fourth solution = (8/π,1)
iii)
Given equation is x = 4y
Put x = 0 then
0=4y
=> y = 0/4
=> y = 0
The first solution = (0,0)
Put y = 1 then
x = 4(1)
=> x = 4
The second solution = (4,1)
Put x = 1 then
1 = 4y
=> y = 1/4
The third solution = (1,1/4)
Put y= -1 then
x= 4(-1)
=> x = -4
The fourth solution = (-1,-4)
3)
Given equation is x-2y =4
I.(0,2):-
Put x = 0 and y = 2 then LHS
=> 0-2(2)
=> 0-4
=> -4
LHS ≠ RHS.
(0,2) is not a solution.
ii)(2,0):-
=>Put x = 2 and y = 0 then LHS
=> 2-2(0)
=> 2-0
=> 2
LHS ≠ RHS.
(2,0) is not a solution.
iii)(4,0)
Put x = 4 and y = 0 then LHS
=> 4-2(0)
=> 4-0
=> 4
LHS = RHS.
(4,0) is a solution.
iv)(√2,4√2):-
Put x = √2 and y = 4√2 then LHS
=> √2-2(4√2)
=> √2-8√2
=> (1-8)√2
=> -7√2
LHS ≠ RHS.
(√2,4√2) is not solution.
v)(1,1):-
Put x =1 and y = 1 then LHS
=> 1-2(1)
=> 1-2
=> -2
LHS ≠ RHS.
(1,1) is not solution.
4)
Given equation is 2x+3y = k
If x = 2 and y = 1 is a solution then it satisfies the given equation.
=> 2(2)+3(1) = k
=> 4+3 = k
=> 7=k
Therefore,k = 7
The value of k = 7