Multiplying the first equation by 15y, .. 45y-21y-6x=75y-25x-45; and by transposition, 51y-19x=45. Multiplying the second equation by 2x+5, 8x+20+30xy+75y 2xy+5y 6x-2 1 107 8 107_8x+20+30xy+75y, .. (Art. 186) 5y+ 8 6x-2 and multiplying by 6x-2, we shall have and 321x-107=32x+340y+80; .. by transposition, 340y-289x=-187. The coefficients of y in this case, having aliquot parts; multiplying the first by 20, and the last by 3, 1020y-380x= 900, and 1020y-867x=-561; .. by subtraction, 487x=1461, and x=3; consequently, 51y=45+19x=45+57=102; Multiplying the first equation by 5+2y, 40x16xy 80+300x+32y+120xY—16xy-107 ; 3y-1 80+300x+32y+120xy .. trans" 40x+107: 3y-1 and multiplying by 3y-1, we shall have 120xy-40x+321y-107=80+300x+32y+ 120xy; .. by transposition, 289y-340x=187. And from the second equation, 27x2-12y +15x+2y+2=27x2 — 12y2+38 ; .. by transposition, 15x+2y=36 ; whence, the coefficients of a having aliquot parts, multiplying the first equation by 3, and the second 867y-1020x=561, and 136y+1020x=2448; .. by addition, 1003y=3009, and y=3; by 68, consequently, 15x=36-2y=36-6=30; and by division, x=2. to find the values of x and y. Ans. x=21, and y=20 3x -1 Ex. 10. Given 5 +3y-4=15, and 34—5+2x—8—73,} to find the values of x and y. Ans. x=7, and y=5. 3y-x 5 and 3x+4 2y-35: 3, to find the values of x and y. Ans. x=7, and y=9. Ex. 18. Given 5x+13 8y-3x-5 =9+ 2 6 7x-3y+1, and +7 x+7 34-8 +4x4:21, 3 3 4 Ans. x=7, and y=9. Ex. 20. Given 3x-2y-15, to find the values and y+10x-15::7: 3,5 of x and y. Ans. x=45, and y=60. Ex. 21. Given x+150: y-50:3: 2, to find and x-50: +100 : : 5 the values of x and 3. : 9, Ans. x300, and y=350. Ex. 22. Given (x+5).(y+7)=(x+1)(y−9)+ 112, and 2x+10=3y+1, to find the values of x and y. Ans. x=3, and y=5.. 6x+130-24y2 Ex. 23. Given 3x+6y+1= and 3x 2x-4y+3 151-16x_9xy-110 4y-1 3y-4 to find the values of x and y. Ans. x=9, and ́y=2.. 128x-18y+2171 8x-3y+2 Ex. 24. Given 16x+6y-1= Involving three or more unknown Quantities. 252. When there are three independent simple: equations involving three unknown quantities. RULE. From two of the equations, find a third, which. involves only two of the unknown quantities, by any of the rules in the preceding Section; and in like manner from the preceding equation, and one of the other, another equation which contains the same two unknown quantities may be deduced.. |