Objective Simultaneous Equations

1. By the eliminations of one or more than one variables from the given simultaneous equations, we get such a relation which is __________ of that variable.
2.  At least ________ equations are required for elimination of one variable.
3. In elimination, both equations should have the ________ that has to eliminate.
4. Eliminant or relation shows that the solution set of both equations is not _________.
5. The relation free from x for x-b = 0 and x-d = 0 is ___________.
6. The relation free from x for xt = s and x = t is ___________.

7. The relation free from t for at = x and 2at = y is ______________.
8. The relation independent of ‘x’ for equations x + 1/x = a  and x² + 1/x² = b² is ________.
9. Te relation independent of ‘x’ for equations x + 1/x = m and x³ + 1/x³= n is __________.
10. The relation free from ‘t’ for equations x + t = 3p and x – t = 4q is ____________.
11. The eliminant by eliminating ‘m’ for equations m + bc = x and m – ad = y is _______.
12. The eliminant by elimination y for equations y² = s and y³ = r is ____________.
13. The relation free from y for equation y = 1/2m and y = 4n is ____________.
14. The equation y + 4 = 9 is y –5 =6 are not true for a __________ value of y.
15. A relation independent of ‘t’ from equations t⁵ = d and t³ = b is ___________.
16. A relation independent of ‘x’ from equations x³ – b = 0 and x² + d = 0 is ________.
17. The relation free from ‘x for equations x² + 1 = 3m² and x⁴ + 1 = n⁴ is __________.                                                                                         x²                         x⁴

18. The relation free from ‘y’ for equations √y – 1    = √a and y + 1/y  = b is ___________.                                                                                    √y

19. The relation from ‘y’ for equation x = √2 t and y = √7 t is ____________.
20. The relation free from ‘x’ for equations x + a = 0 and x² + y² = b² is _________.
21. The eliminant by elimination ‘u’ for equations v = u –t and u² = 2vt.
22. The eliminant by eliminating ‘y’ for equations y³ + 1/y³  = m and y³ – 1/y³  = n is _______.
23. The relation free from ‘x’ for equations x – 1 = m and x³ – 1 = 4n³ is _________                                                                                            x                       x³

24. The relation free from ‘x’ for equations x = 3p and x = 1 is __________                                                                                                                               7t

25. The relation free from ‘y’ for equation y² – 1/y² = a and y⁴ + 1/y⁴ = b⁴.