3. Form the pair of linear equations for the following problems and find their solution by substitution method. (i) The difference between two numbers is 26 and one number is three times the other. Find them.

Solution: Let the two numbers be x and y respectively, such that y > x. According to the question, y = 3x ……………… (1) y – x = 26 …………..(2) Substituting the value of (1) into (2), we get 3x – x = 26 x = 13 ……………. (3) Substituting (3) in (1), we get y = 39 Hence, the numbers are 13 and 39. (ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them. Solution: Let the larger angle by xo and smaller angle be yo. We know that the sum of two supplementary pair of angles is always 180o. According to the question, x + y = 180o……………. (1) x – y = 18o ……………..(2) From (1), we get x = 180o – y …………. (3) Substituting (3) in (2), we get 180o – y – y =18o 162o = 2y y = 81o ………….. (4) Using the value of y in (3), we get x = 180o – 81o = 99o