1.

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

Answer»

(i) 2x + y = 7 

If x = 0, 2x + y = 7

2 × 0 + y = 7 

0 + y = 7 

y = 7 

Solution is (0, 7). 

If x = 1, 2x + y = 7 

2 × 1 + y = 7 

2 + y = 7 

y = 7 – 2 = 5 

Solution is (1, 5). 

If x = 2, 2x + y = 7 

2 × 2 + y = 7 

4 + y = 7 

y = 7 – 4 = 3 

Solution is (2, 3). 

If x = 3, 2x + y = 7 

2 × 3 + y = 7 

6 + y = 7 

∴ y = 7 – 6 = 1 

Solution is (3, 1). 

(ii) πx + y = 9 

If x = 0, πx + y = 9 

π × 0 + y = 9 

0 + y = 9 

y = 9 

Solution (x, y) = (0, 0). 

If x = 1, πx + y = 9 

π × 1 + y = 9 

π + y = 9 

y = 9 – π 

Solution (x, y) = (1, 9 – π). 

If y = 0, πx + y = 9 

πx + 0 = 9 

πx = 9 

∴ x = \(\frac{9}{\pi}\)

Solution (x, y) = (\(\frac{9}{\pi}\) , 0). 

If y = 1, πx + y = 9 

πx + 1 = 9 

πx = 9 – 1 

πx = 8 

∴ x = \(\frac{8}{\pi}\)

Solution (x, y) = ( \(\frac{8}{\pi}\),1). 

(iii) x = 4y 

If x = 0, x = 4y 

0 = 4y 

4y = 0 

∴ y = \(\frac{0}{4}\)=∞ 

∴ Solution (x, y) = (0, ∞). 

If x = 1, x = 4y 

1 = 4y 

4y = 1 

∴ y = \(\frac{1}{4}\)

∴ Solution (x, y) = (1, \(\frac{1}{4}\)). 

If x = 2, x = 4y 

2 = 4y 

4y = 2 

∴ y = \(\frac{4}{2}\)

∴ y = \(\frac{1}{2}\)

Solution (x, y) = (2, \(\frac{1}{2}\)). 

If x = 4, 

x = 4y 

4 = 4y 

4y = 4 

∴ y = \(\frac{4}{4}\)

∴ y = 1 

∴ Solution (x, y) = (4, 1).



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