Page:Elementary algebra (1896).djvu/170

152 Rh 7. {2}{3}x-{1}{12}y = 3, 4x-y = 20 10. {x}{7} + {y}{5}= 1, x + {y}{3} = 4. 12. {x}{5} -{y}{4} =0, 3x + y = 17. 8. x-y = 4, x + {y}{3} = 4. 9. 2x + y = 0, y-3x = 8 11. 3x-7y=0, x + y = 7 13. {3x-1}{2}-{y}{4} ={7}{2}, x + 3y=9 14. {x}{3} + {y}{4}=3x-7y-37 = 0. 15. {x+1}{10} ={3y-5}{2} = {x-y}{8}

SIMULTANEOUS EQUATIONS INVOLVING THREE UNKNOWN QUANTITIES.

175. In order to solve simultaneous equations which contain two unknown quantities we have seen that we must have two equations. Similarly, we find that in order to solve simultaneous equations which contain three unknown quantities we must have three equations.

Rule. Eliminate one of the unknowns from any pair of the equations, and then eliminate the same unknown from another pair. Two equations involving two unknowns are thus obtained, which may he solved by the rules already given. The remaining unknown is then found by substituting in any one of the given equations.

Ex.1. Solve 6x + 2y-5z = 13 (1), 3x + 3y -2z = 13 (2), 7x + 5y-3z=26 (3).

Choose y as the unknown to be eliminated.

Multiply (1) by 3 and (2) by 2, 18 x + 6 y - 15 z = 39, 6x + 6y - 4z= 26; subtracting, 12 x - 11z = 13 (4).

Again, multiply (1) by 5 and (3) by 2, 30x+ 10y-25z = 65, 14x+10y - 6z = 52, subtracting, 16x-19z = 13 (5).