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Question:

Write four solutions for each of the following equations: (i) 2x+y=7 (ii) πx+y=9 (iii) x=4y

Solution:

(i) 2x+y=7
y = 7-2x
When x=0, then y = 7-20
y = 7-0
y = 7
When x=1 then y = 7-2
1
y = 7-2
y = 5
When x=2 then y = 7-22
y = 7-4
y = 3
When x=3 then y = 7-2
3
y = 7-6
y = 1
Hence, four solutions for equation 2x+y=7 are (0,7),(1,5),(2,3),(3,1)
(ii) πx+y=9
y = 9-πx
When x=1 then y = 9-π1
y = 9-π
When x=0 then y = 9-π
0
y = 9
When x=2 then y = 9-π2
y = 9-2π
When x=-1 then y = 9-π
-1
y = 9+π
Hence, four solutions for equation πx+y=9 are (1, 9-π), (0,9), (2, 9-2π), (-1, 9+π)
(iii) x=4y
When y=0, then x=40
x=0
When y=1 then x=4
1
x=4
When y=2 then x=42
x=8
When y=-1 then x=4
-1
x=-4
Hence, four solutions for equation x=4y are (0,0),(4,1),(8,2),(-4,-1). The provided answer is one of the various possible solutions. This question might have other solutions too.