Page:Elementary algebra (1896).djvu/168

150 Rh ELIMINATION BY COMPARISON.

173. Ex. Solve x+15y = 53 (1), y+3x = 27 (2).

From (1) x = 53 - 15y, and from (2) x = {27-y}{ 3 }

Placing these values of x equal to each other, we have 53-15y = {27-y}{ 3 }

Whence 159 - 45 y = 27 - y, and 44 y = 132 ; y = 3.

Substituting this value in either (1) or (2) gives x = 8.

Rule. From each equation find the value of the unknown quantity to he eliminated in terms of the other and known quantities; then form an equation with these values, and reduce.

EXAMPLES XVII. a.

Solve the equations :

1. 3 x + 4y =10, 8. 15 x +7y =20, 15. 39x-8y = 99, 4x + y = 9. 9x+15y = 39. 52x-15y = 80. 2. x + 2y = 13, 9. 14x -3y = 39, 16. 5x=7y-21, 3x + y = 14. 6x + 17y = 35. 21x-9y = 75. 3. 4x + 7y = 29, 10. 28 x - 23 y = 33, 17. 6y-5x=18, x + 3y = 11. 63 x- 25y = 101. 12x-9y = 0. 4. 2x-y = 9, 11. 35x+17y = 86, 18. 8x = 5y, 3 X - 7 y = 19. 56 X - 13 y = 17. 13 x = 8 y + 1. 5. 5x + 6y=17, 12. 15x + 77y = 92, 19. 3x=7y, 6x + 5y = 16. 55x-33y = 22. 12y = 5x-1. 6. 2x + y=10, 13. 5x-7y = 0, 20. 19x+17y = 0, 7x + 8y = 53. 7x + 5y = 74. 2x-y = 53. 7. 8x-y = 34, 14. 21x-50y = 60, 21. 93x + 15y = 123, x + 8y = 53. 28x-27y = 199. 15x + 93y = 201.