Write two solutions for each of the following equations:
(i) 3x+4y =7
(ii) x=6y
(iii) x+πy =4
(iv) x-y =4
Answers
(i) Given : 3x + 4y = 7.................(1)
On putting x = 0 in equation 1
3x + 4y = 7
3 × 0 + 4y = 7
0 + 4y = 7
4y = 7
y = 7/4
So( 0, 7/4) is a solution of given equation.
On putting y = 0 in equation 1
3x + 4 × 0 = 7
3x + 0 = 7
3x = 7
x = 7/3
So (7/3, 0) is a solution of given equation.
Hence, 2 out of the infinitely many solutions of the given equation are(0,7/4), (7/3,0).
(ii) x = 6y
Let x = 0
x = 6y
0 = 6y
y = 0/6
y = 0
(0,0) is the solution.
Let x = 1
x = 6y
1= 6y
y= 1/6
(1,1/6) is the solution.
Hence, 2 out of the infinitely many solutions of the given equation are(0,0), (1,1/6).
(iii) x + πy = 4
let x = 0
x + πy = 4
0 + πy = 4
πy = 4
y = 4/π
(0, 4/π) is the solution.
Let y = 0
x + πy = 4
x + 0(y) = 4
x + 0 = 4
x = 4
(4, 0) is the solution.
Hence, 4 out of the infinitely many solutions of the given equation are (0, 4/π), (4, 0).
(iv) x - y = 4
Let x = 0
x - y = 4
0 - y = 4
-y = 4
y = - 4
(0,- 4) is the solution.
Let x = 1
x - y = 4
1 - y = 4
-y = 4 - 1
-y = 3
y = - 3
(1,- 3) is the solution.
Hence, 4 out of the infinitely many solutions of the given equation are(0,- 4), (1,- 3).
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Step-by-step explanation:
for equation 3x + 4y = 7
let the value of x be 0 and 2
the two solutions are :
3(0) + 4y = 7
4y= 7
y= 4/7
now x=2
3(2) + 4y=7
4y=7-6
y=1/4
for equarion x=6y
let y=1
x=6(1)
x =6(1)
let y=2
x=6(2)
x=12