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