write four solutions for each of th following equations 2x+y=7, ♫x+y=9, x=4Y
Answers
For finding the solutions of linear equation in two variables we use the following steps:
1.Put an put an arbitrary value of x or y in given equation and find the corresponding value of other variable.
Thus, we get one pair of solution of given equation.
2.Repeat repeat step 1 for another arbitrary value of x or y and get other pair of solution of given equation.
For convenience , we put x= 0 & get corresponding value of y to find one pair of solution.
Also we put y = 0 and get corresponding value of x to find 2nd pair solution.
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Solution:
(a)2x + y = 7......(1)
On putting x=0 in equation 1
2x+y=7
2×0+y=7
0+y=7
Y=7
So( 0, 7) is a solution of given equation.
let y=0
2x+y=7
2x+0=7
2x=7
X= 7/2
So(7/2,0) is a solution of given equation.
let x = 1
2x+y=7
2×1+y=7
2+y=7
Y= 7-2
Y=5
(1,5) is the solution.
let x = 2
2x+y=7
2×2+y=7
4+y=7
Y= 7-4
Y= 3
The solution is (2,3)
Hence, 4 out of the infinitely many solutions of the given equation are(0,7), (7/2,0),(1,5),(2,3)
(b) πx + y = 9
let x = 0
πx + y = 9
π×0+y =9
0+y= 9
Y=9
(0,9) is the solution.
Let y = 0
πx + y = 9
πx+0=9
πx=9
x= 9/π
(9/π,0) is the solution.
Let x = 1
πx + y = 9
π×1+y=9
π+y=9
Y= 9-π
(1,9-π) is the solution.
Let x = -1
πx + y = 9
π×-1+y=9
-π+y=9
Y= 9+π
(-1,9+π) is the solution.
Hence, 4 out of the infinitely many solutions of the given equation are(0,9), (9/π,0),(1,9-π),(-1,9+π)
(c) x= 4y
Let x = 0
X=4y
0=4y
Y=0/4=0
Y=0
(0,0) is the solution.
Let x= 1
X=4y
1=4y
Y= 1/4
(1,1/4) is the solution.
Let y = 1
X=4y
X=4×1
X=4
(4,1) is the solution.
Let x = 2
X=4y
2=4y
Y=2/4
Y=1/2
(2,1/2) is the solution.
Hence, 4 out of the infinitely many solutions of the given equation are(0,0), (1,1/4),(4,1),(2,1/2)
Answer:
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