(3x+4y_5y-3x-2x+3y 3y-2x

201. In many equations it is advantageous at first not to consider x and y as unknown quantities, but some expressions

=

Check.+1+2 = 3; 1⁄2-5-14.

Examples of this type, however, can also be solved by the regular method, provided they do not involve more than two unknown quantities. Clearing (1) and (2) of fractions,

2 × (5),

3y+8x=3xy.

(4)

(5)

(6)

(7)

Ex. 2. Solve

1183

(1)

6 xy +

21. Solve the equations

ax + by = c,

px+qy=r,

and from the results find by numerical substitution the roots of

Exs. 1-4, page 188.

22. Find a and s in terms of n, d, and l if

23. From the same simultaneous equations find d in terms of a, n, and l.

24. From the same equations find s in terms of a, d, and 7. 25. From the same system of equations find n in terms of a, l, and s.

SIMULTANEOUS EQUATIONS INVOLVING MORE THAN TWO UNKNOWN QUANTITIES

203. To solve equations containing three unknown quantities three simultaneous independent equations must be given.

By eliminating one unknown quantity from any pair of equations, and the same unknown quantity from another pair, the problem is reduced to the solution of two simultaneous equations containing two unknown quantities.

Similarly four equations, containing four unknown quantities, are reduced to three equations containing three unknown quantities, etc.

Ex. 1. Solve the following system of equations:

2x-3y+4z = 8.

3x+4y-5z=-4.

4x-6y+3% = 1.

(1)

(2)

(3)