Page 1 Exercise 3B 1. Solve for x and y: x + y = 3, 4x 3y = 26 Sol: The given system of equation is: 4x On multiplying (i) by 3, we get: Page 2 Exercise 3B 1. Solve for x and y: x + y = 3, 4x 3y = 26 Sol: The given system of equation is: 4x On multiplying (i) by 3, we get: On adding (ii) and (iii), we get: 7x = 35 x = 5 On substituting the value of x = 5 in (i), we get: 5 + y = 3 y = (3 5) = -2 Hence, the solution is x = 5 and y = -2 2. Solve for x and y: x y = 3, + = 6 Sol: The given system of equations is x y = 3 + = 6 From (i), write y in terms of x to get y = x 3 Substituting y = x 3 in (ii), we get + = 6 2x + 3(x 3) = 36 2x + 3x 9 = 36 x = = 9 Now, substituting x = 9 in (i), we have 9 y = 3 y = 9 3 = 6 Hence, x = 9 and y = 6. 3. Solve for x and y: 2x + 3y = 0, 3x + 4y = 5 Sol: The given system of equation is: On multiplying (i) by 4 and (ii) by 3, we get: iii) On subtracting (iii) from (iv) we get: Page 3 Exercise 3B 1. Solve for x and y: x + y = 3, 4x 3y = 26 Sol: The given system of equation is: 4x On multiplying (i) by 3, we get: On adding (ii) and (iii), we get: 7x = 35 x = 5 On substituting the value of x = 5 in (i), we get: 5 + y = 3 y = (3 5) = -2 Hence, the solution is x = 5 and y = -2 2. Solve for x and y: x y = 3, + = 6 Sol: The given system of equations is x y = 3 + = 6 From (i), write y in terms of x to get y = x 3 Substituting y = x 3 in (ii), we get + = 6 2x + 3(x 3) = 36 2x + 3x 9 = 36 x = = 9 Now, substituting x = 9 in (i), we have 9 y = 3 y = 9 3 = 6 Hence, x = 9 and y = 6. 3. Solve for x and y: 2x + 3y = 0, 3x + 4y = 5 Sol: The given system of equation is: On multiplying (i) by 4 and (ii) by 3, we get: iii) On subtracting (iii) from (iv) we get: x = 15 On substituting the value of x = 15 in (i), we get: 30 + 3y = 0 3y = -30 y = -10 Hence, the solution is x = 15 and y = -10. 4. Solve for x and y: 2x - 3y = 13, 7x - 2y = 20 Sol: The given system of equation is: 2x - 7x - On multiplying (i) by 2 and (ii) by 3, we get: 4x - 21x - On subtracting (iii) from (iv) we get: 17x = (60 26) = 34 x = 2 On substituting the value of x = 2 in (i), we get: 4 3y = 13 3y = (4 13) = -9 y = -3 Hence, the solution is x = 2 and y = -3. 5. Solve for x and y: 3x - 5y - 19 = 0, -7x + 3y + 1 = 0 Sol: The given system of equation is: 3x - 5y - - On multiplying (i) by 3 and (ii) by 5, we get: 9x - -35x + 15y = - On subtracting (iii) from (iv) we get: -26x = (57 5) = 52 x = -2 On substituting the value of x = -2 in (i), we get: Page 4 Exercise 3B 1. Solve for x and y: x + y = 3, 4x 3y = 26 Sol: The given system of equation is: 4x On multiplying (i) by 3, we get: On adding (ii) and (iii), we get: 7x = 35 x = 5 On substituting the value of x = 5 in (i), we get: 5 + y = 3 y = (3 5) = -2 Hence, the solution is x = 5 and y = -2 2. Solve for x and y: x y = 3, + = 6 Sol: The given system of equations is x y = 3 + = 6 From (i), write y in terms of x to get y = x 3 Substituting y = x 3 in (ii), we get + = 6 2x + 3(x 3) = 36 2x + 3x 9 = 36 x = = 9 Now, substituting x = 9 in (i), we have 9 y = 3 y = 9 3 = 6 Hence, x = 9 and y = 6. 3. Solve for x and y: 2x + 3y = 0, 3x + 4y = 5 Sol: The given system of equation is: On multiplying (i) by 4 and (ii) by 3, we get: iii) On subtracting (iii) from (iv) we get: x = 15 On substituting the value of x = 15 in (i), we get: 30 + 3y = 0 3y = -30 y = -10 Hence, the solution is x = 15 and y = -10. 4. Solve for x and y: 2x - 3y = 13, 7x - 2y = 20 Sol: The given system of equation is: 2x - 7x - On multiplying (i) by 2 and (ii) by 3, we get: 4x - 21x - On subtracting (iii) from (iv) we get: 17x = (60 26) = 34 x = 2 On substituting the value of x = 2 in (i), we get: 4 3y = 13 3y = (4 13) = -9 y = -3 Hence, the solution is x = 2 and y = -3. 5. Solve for x and y: 3x - 5y - 19 = 0, -7x + 3y + 1 = 0 Sol: The given system of equation is: 3x - 5y - - On multiplying (i) by 3 and (ii) by 5, we get: 9x - -35x + 15y = - On subtracting (iii) from (iv) we get: -26x = (57 5) = 52 x = -2 On substituting the value of x = -2 in (i), we get: 6 5y 19 = 0 5y = ( 6 19) = -25 y = -5 Hence, the solution is x = -2 and y = -5. 6. Solve for x and y: 2x y + 3 = 0, 3x 7y + 10 = 0 Sol: The given system of equation is: 2x 3x From (i), write y in terms of x to get y=2x + 3 Substituting y = 2x + 3 in (ii), we get 3x 7(2x + 3) + 10 = 0 3x 14x 21 + 10 = 0 -7x = 21 10 = 11 x = Now substituting x = in (i), we have y + 3 = 0 y = 3 - = - Hence, x = and y = . 7. Solve for x and y: 9x - 2y = 108, 3x + 7y = 105 Sol: The given system of equation can be written as: 9x - On multiplying (i) by 7 and (ii) by 2, we get: 63x + 6x = 108 × 7 + 105 × 2 69x = 966 x = = 14 Now, substituting x = 14 in (i), we get: 9 × 14 2y = 108 2y = 126 108 Page 5 Exercise 3B 1. Solve for x and y: x + y = 3, 4x 3y = 26 Sol: The given system of equation is: 4x On multiplying (i) by 3, we get: On adding (ii) and (iii), we get: 7x = 35 x = 5 On substituting the value of x = 5 in (i), we get: 5 + y = 3 y = (3 5) = -2 Hence, the solution is x = 5 and y = -2 2. Solve for x and y: x y = 3, + = 6 Sol: The given system of equations is x y = 3 + = 6 From (i), write y in terms of x to get y = x 3 Substituting y = x 3 in (ii), we get + = 6 2x + 3(x 3) = 36 2x + 3x 9 = 36 x = = 9 Now, substituting x = 9 in (i), we have 9 y = 3 y = 9 3 = 6 Hence, x = 9 and y = 6. 3. Solve for x and y: 2x + 3y = 0, 3x + 4y = 5 Sol: The given system of equation is: On multiplying (i) by 4 and (ii) by 3, we get: iii) On subtracting (iii) from (iv) we get: x = 15 On substituting the value of x = 15 in (i), we get: 30 + 3y = 0 3y = -30 y = -10 Hence, the solution is x = 15 and y = -10. 4. Solve for x and y: 2x - 3y = 13, 7x - 2y = 20 Sol: The given system of equation is: 2x - 7x - On multiplying (i) by 2 and (ii) by 3, we get: 4x - 21x - On subtracting (iii) from (iv) we get: 17x = (60 26) = 34 x = 2 On substituting the value of x = 2 in (i), we get: 4 3y = 13 3y = (4 13) = -9 y = -3 Hence, the solution is x = 2 and y = -3. 5. Solve for x and y: 3x - 5y - 19 = 0, -7x + 3y + 1 = 0 Sol: The given system of equation is: 3x - 5y - - On multiplying (i) by 3 and (ii) by 5, we get: 9x - -35x + 15y = - On subtracting (iii) from (iv) we get: -26x = (57 5) = 52 x = -2 On substituting the value of x = -2 in (i), we get: 6 5y 19 = 0 5y = ( 6 19) = -25 y = -5 Hence, the solution is x = -2 and y = -5. 6. Solve for x and y: 2x y + 3 = 0, 3x 7y + 10 = 0 Sol: The given system of equation is: 2x 3x From (i), write y in terms of x to get y=2x + 3 Substituting y = 2x + 3 in (ii), we get 3x 7(2x + 3) + 10 = 0 3x 14x 21 + 10 = 0 -7x = 21 10 = 11 x = Now substituting x = in (i), we have y + 3 = 0 y = 3 - = - Hence, x = and y = . 7. Solve for x and y: 9x - 2y = 108, 3x + 7y = 105 Sol: The given system of equation can be written as: 9x - On multiplying (i) by 7 and (ii) by 2, we get: 63x + 6x = 108 × 7 + 105 × 2 69x = 966 x = = 14 Now, substituting x = 14 in (i), we get: 9 × 14 2y = 108 2y = 126 108 y = = 9 Hence, x = 14 and y = 9. 8. Solve for x and y: + = 11, - + 7 = 0 Sol: The given equations are: + = 11 and - + 7 = 0 5x 2y = - On multiplying (i) by 2 and (ii) by 3, we get: 15x 6y = - On adding (iii) and (iv), we get: 23x = 138 x = 6 On substituting x = 6 in (i), we get: 24 + 3y = 132 3y = (132 24) = 108 y = 36 Hence, the solution is x = 6 and y = 36. 9. Solve for x and y: 4x - 3y = 8, 6x - y = Sol: The given system of equation is: 4x - 6x - y = On multiplying (ii) by 3, we get: 18x On subtracting (iii) from (i) we get: -14x = -21 x = = Now, substituting the value of x = in (i), we get:Read More

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