Page:Elementary algebra (1896).djvu/172

154 Rh Thus the combination of equations (1) and (2) leads us to an equation which is identical with (3), and so to find x and y we have but a single equation 7 x - 4 y = 8, the solution of which is indeterminate. [Art. 167.]

In this and similar cases the anomaly arises from the fact that the equations are not independent; in other words, one equation is deducible from the others, and therefore contains no relation between the unknown quantities which is not already implied in the other equations.

EXAMPLES XVII. c.

1. x+ 2y + 2z = 11, 2x+ y+ z=7, 3x + 4y+ z= 14.

9. 3x-4y = 6z-16, 4 x - y -z=5, x = 3y + 2(z-1).

2. x + 3y+4z = 14, x+2y+ z = 7, 2x+ y + 2z=2

10. 5x + 2y= 14, y-6z=-15, x + 2y +z = 0.

3. x + 4y + 3z = 17, 3x + 3y+ z= 16, 2x + 2y+ z= 11.

11. x-{y}{6} = 6, y- {z}{7} = 8. z-{x}{2} = 10.

4. 3x-2y+z = 2, 2x+3y- z= 5, x + y + z = 6. 12. y+^-^-fa3-x-fy^ x+ y +^2 = 27.

5. 2x+ y+ z= 16, x + 2y+ z= 9, x+ y + 2z = 3.

13. ^-^=^-^=50 4 3 2 y+z=2x+ 1.

6. x-2y + 3z=2. 2x-3y+ z= 1, 3x- y+2z = 9.

14. 2x + 3 y = 5, 2z- y=1, 7x - 9z = 3.

7. 3x + 2y- z=20, 2x + 3 y + 6z = 70, x - y + 6z = 41.

15. (x+z-5)=y-z = 2x-11 = 9-(x + 2z)

8. 2x+3y + 4z = 20, 3x+4y +5z = 26, 3x+ 5y + 6z = 31.

16. x + 20= {}{} + 10 = 2z + 5 = 110-( y+z)

176. Definition. If the product of two quantities be equal to unity, each is said to be the reciprocal of the other. Thus if ab = 1, a and b are reciprocals. They are so called