x+2.(3x ---2)=17, or x+6x-4=17; .. by transposition, 7x=17+4=21, 21 by division, x= ...=3; 7? and .. y=3x-2=3X3--2=9--2=7. =} Ex. 2. Given to find the 5x+10=78+y, S values of a and y. From the first equation, y=60-3x; Let the value of y be substituted in the second equation, and it becomes, 5x+10=78+(60-32) Then, by transposition, 8x=78+60-10;. 128 8 ..y=12. rx+y=66—24, , to find the va 3 Ex. 3. Given lues of x and -Y -62– 2x, y. 3 Mult. the 1st equation by 3, then x+y=198-by: .. (1); 2nd by 3, then x-y=186-63 .. (2), (2; From equation (1), we have x=198-7y, (2), 70-y=186 ; By substituting the above value of x, in the last equation, it becomes 7(198—7y)-y=186, or, 1386-49y-y=186 ; by transposition, -50y=186--1336=-1200, by changing the signs, 50y=1200, 1200 .. by division, y= =24. 50 Whence, v=198-7y=198-7X24=198-168, ..x—30. *=} Sx+2y=80, Ex. 4. Given to find the values ut y=60, of x and y. From the second equation, x=60-y: = By substituting this value of x in the 1st equation, we have, 60-y+2y=80, by transposition, y=80-60, ..y=20. And x=60-y=(by substitution) 60-_20, =40. { Ex. 5. Given x+2y=17,2 to find the va 3x — y= 2, lues of x and y. From the 1st equation, x=17--2y. 3(17 — 2y) — y=2, .. by division, y=7, whence, x=17--2y=17--2X7=17-14, .. y=3. Ex. 6. Given ac +y =5, to find the values of x and yo From the first equation, s=5-y, squaring both sides, xo=(5-3). And by substituting this value for to in the sea cond equation, it becomes, (5-y) - Yo=4, by reduction, 25+10y=5, by transposition, 10y=20, .. by division, y=2. Whence, a=54-y=5--2=3. (6+8y=194, (b+8x=131 , of and y. 8 =, 8 Ex. 7. Given to find the values y x . 8 x+64y=1552, s'. by transposition, x=1552-64y. And substituting this value for x, in the second equation, it becomes, y +8(1552—64y)=131, by reduction, y+99328-4096y=1048, by transposition, 4095y=98280, 98280 by division, y 4095 ..y=24. Whence x=1552-64y=1552-64 X 24, or x=1552-1536 ; mix= =16. The value of y might be found from the second equation, in terms of x and the known quantities ; which value of y substituted for it in the first, an equation would arise involving only x, the value of which might be found; and therefore the value of y also may be obtained by substitution. 6x-5Y=6, to 5x+6y Ex. 8. Given -=27, and 3 4 the values of w and y Ans. x=9, and y=6. Ex. 9. Given 15y +45x=300, and +-15y=36, to find the values of x and y. Ans. x=6, and y=2. Ex. 10. Given 3x+y=60, and 5x+10=78+y, to find the values of w and y. Ans. x=16, and y=12. Ex. 11. Given 10x --3y=38, and 3x-y=11, to find the values of x and y. Ans. x=5, and y=4. Ex. 12. Given x+y=193-6y, and x-y=186 --6c, to find the values of x and y. Ans. =30, and y=24. . y y = , = 8 8 to find the values of wand y. • Ans. «=16, and y=24. 20* . 3. 2 values of x and y Ans. x=6, and y=12. Es. 15. Given 4x+y=34, and 4y +x=16, to find the values of x and y. Ans. x=8, and y=2. Ex. 16. Given 3x +2y=54, and x:y::4:3, to find the values of x and Yo Ans. r=12, and y=9. Ex. 17. Given = 4 3 23, to find the values of cand y. Ans. x=4, and y=3, Ex. 13. Given + y = 26, and +0x = 131, Ex. 14. Giyen +%=7, and +9 =8, to find the = x+8 +6y=21, and 9+ 6 + 5x = y6 RULE III. 249. Find the value of the same unknown quantiiy in terms of the other and known quantities, in each of the equations; then, let the two values, thus found, be put equal to each other; an equation arises involving only one unknown quantity; the value of which may be found, and therefore, that of the other unknown quantity, as in the preceding rules. This rule depends upon the well known axiom, (Art 47); and the two preceding methods are founded on principles which are equally simple and obvious. s x+3y=100, Ex. 1. Given to find the va12 + y=100, 5 lues of x and y. From the first equation, x=100-3y, = and from the second, x= 3 2 100-y 100—4 = 100-3y, C 2 Multiplying by 2, 100-y=200—6y, by transposition, by-y=200-100, or, 5y=100; ... by division, y=20. whence, x=100 - 3y=100—3 X 20; .. x=40. Here, two values of y might have been found, which would have given an equation involving only x; and from the solution of this new equation, a value of , and therefore of y, might be found, |