subtracting the upper equation from the lower,

we have 48y=693-21=672,

y+5

4

to find the

values of x

+10x=192, and y.

Clearing the first equation of fractions,

x+2+24y=93;

by transposition, x+24y=91 Clearing the second equation of fractions,

y+5+40x=768;

: (1),

.. by transposition, 40x+y=763 . . . (2.)

Multiplying equation (1) by 40, and subtracting equation (2) from it, 40x960y=3640;

40x+ y= 763;

.. 959y=2877,

and by division, y=3;

From equation (1), x=91-24y,
.. by substitution, x=91-24 X 3,

If from equation (2), multiplied by 24, equation (1) had been subtracted, an equation would have arisen involving only x, the value of which might be determined, and this being substituted in either of the equations, the value of y might also be found.

Mult. the 1st equation by 2, then +4y-24;

Or, the values of x and y may be found thus ; From the first equation subtract the second and we have 4y=8,..y=2.

Add the first equation to the second,

and.. 16.

Ex. 10. Given 4x+3y=31, and 3x+2y=22; to

find the values of x and y.

Ans. x4, y=5,

to find the values of x and y.

Ex. 11. Given 5x-4y-19, and 4x+2y=36,

2y=2, and

RULE II.

248. Find the value of one of the unknown quantities, in terms of the other and known quantities, in the more simple of the two equations; and substitute this value instead of the quantity itself in the other equation; thus an equation is obtained, in which there is only one unknown quantity; the value of which may be found as in the last Rule.

Ex. 1. Given

lues of x and y.

-From the first equation, x=17-2yz

"Substituting therefore this value of x in the se

cond equation,

3.(17-2y)-y=2,

or 51-6y-y=2;

... by changing the signs, and transposing;

7y=51-2=49,

... by division, y=7;

whence, x=17-2y-17-14-3.

Here a value of y might be determined from either equation, and substituted in the other; from which would arise an equation involving only a, the value of which might be found; and therefore the value of y also might be obtained by substitution, thus;

From the second equation, y=3x-2; substituting therefore this value of y in the first equation; we have,