36x-6x+3y=10-4y, or 30x+7y=10;

equation (2) becomes (with L. c. D. 60)

50-20y=15x-15y-120-6x-6y+12, or 9x+y=-158;

from (2),

from (1),

substitute in (2); then

- 63x+7y=-1106,

30x+7y=10;

..

-93x=1116, or x=12,

- 108+y=-158; .. y= −50.

5. Let the prices of the two sorts be x pence and y pence per lb. respectively;

7. Let x £s and y £s be the prices of A's and B's houses respectively;

8. Let x years and y years be the respective ages;

9. Let x years and y years be the respective ages;

10. Let x years and y years be the respective ages;

11. Let x years and y years be the respective ages;

then

and

.. by subtraction,

also, from (1),

x-6=12 (y-6),

x+3=3(y+3);

-9=9y-81, or y=8,

x-6=24, or x=30.

12. Let x and y be the numbers of persons in each class;

then

and

from (1), from (2),

and

x+y=36,
5y
3x + =100;
2

6x+6y=216,

6x+5y=200;

.. y=16; and from (1), x=20.

13. Let x be the number of oxen, and y the number of sheep;

from (1), from (2),

... from (1),

.. x+y=35,

25x 9y

+ =1911;

2 4

9x+9y=315,

50x+9y=766;

.. 41x=451; or x=11;
y=24.

15. Let x and y be the digits, so that 10x+y is the number;

16. Let x and y be the digits, so that 10x+y is the number;

17.

then

also

from (1),

from (2),

Let x and y be the digits, so that 10x+y is the number;

.. by addition

10x+y=7(x+y),

10y+x=10 (x-y)+6;

3x-6y=0, or 9x-18y=0;

- 9x+20y=6;

.. by substitution in (1),

2y=6, or y=3;

x= =6; hence the number is 63.

18. Let x be the first digit, and y the middle digit;

then

and

from (1),

from (2),

x+y+x=7,

100x+10y+x+90=100y+10x+x;

2x+y=7,

90x-90y=-90, or x-y= −1;
.. 3x=6, or x=2;

also from (1), y=3; hence the number is 232.

19. Let x £s and y £s be the prices of a sheep and a calf respectively;

20. Let x feet be the length of the rectangle, and let y feet be its width;

21. Let x and y be the numbers of the two sorts;

(because each of these represents the value of the oranges in pence);