(Q.1) Draw the graph of the following pair of linear equations. ( I ) 3x + y – 5 = 0 2x – y– 5 = 0 ( ii ) x + y = 7 2x – 3y = 9 ( iii ) 4x + 5y = 9 8x + 10y = 18 ( iv ) x + 2y + 5 = 0 3x + 6y + 15 = 0 (v ) 2x + 3 y = 15 4x + 6y = 24 (vi ) 4x + 2y = 10 6x + 3y = 6 ( Q. 2) Find the value of x and y . ( I) x + 2y = 3 7x – 5y = 2 ( ii ) 2x + 3y = 8 x + 2y = 5 ( iii ) 2x – 3y = 12 x + 2y = –1
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Geometrically the length of a diagonal across a square with sides of one unit of length; this follows the Pythagorean theorem. It was probably the first number known to be irrational.[citation needed]
As a good rational approximation for the square root of two, with a reasonably small denominator, the fraction 99/70 (≈ 1.4142857) is sometimes used.
The sequence A002193 in the OEIS consists of the digits in the decimal expansion of the square root of 2, here truncated to 65 decimal places:
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