multiplying the first of these equations by 7, and the second by 3, 35x-21y 154; by subtraction, 26x = 208; .. x=8, whence, by transposing the equation (A), and substituting the value of x therein, 3y=5x-22-40-22-18; .. y=6. Multiplying the first equation by 20, by transposition, 8x-5x-4y-10y=10+120-150, or 3x-14y=-20. Multiplying the second equation by 12, 144-3x-3y=2x+6y+48; by transposition, -3x-2x-3y—6y=48—144, or 5x+9y=96; multiplying this equation by 3, and the other by 5, 15x+27y= 288; and 15x-70y=-100; by subtraction, 97y= 388; % y=4; whence, by transposition and substitution, 5x=96-9y=96-36-60;.'. x=12. Multiplying the first equation by 4, and the second by 3, substituting this value of x, in the equation (A), 4b+c+by=126; by transposition, by-12b-4b—c=8b—c; Multiplying the first equation by 6, the least com mon multiple of 6 and 2, Also, multiplying this equation by 20, by transposition, 240x+5x-24x-120y-24y=1440 -12-20, or 221x-144y=1408. (A) From the second equation, Theorem 2, Substituting this value of x, in the equation (A), it becomes, 7072y 10 -144y=1408; ..7072y-1440y=14080, or 5632y=14080; .. y = 21. Substituting this value of y, in the equation (B), EXAMPLES FOR PRACTICE, In Simple Equations of two unknown Quantities. 1. Given 4x+6y=36, to find the values of x and y. iven and 2x+5y=26, S Ans. x=3. y=4. 3. Given 5x+4y=22, to find the values of x and y. and 7x-5=3y, S Ans. { x=2. y=3. 4. Given 4x-y+4=21, 2 to find the values of x and 5x+3y—942, and y. |