2 4. Let 3x2-10x8x+x* be given; to find *. 2 +6ax ; to find x. First, dividing the whole by zax, we shall have 2x-46=x+2 And then 2x-x=2+46 Whence x=2+46. And then 3x-9+2x-120-3x-57 "That is, 8x72, or x==9. 8. Let √x+5=7 be given; to find x. 1 9. Let " Ans. 11 cd+a-b. 3 2. Given zy-a+b=cd; to find y. Ans. y= 3. Given 6-2x+10=20-3-2; to find x. a 4. Given 3ax+--3-bx-a; to find x. 2 Ans. 2. 6-34 Ans. x= 6a-26 7. Given √ 12+x=2+√x; to find x. Ans. x=4. 8. Given I ; to find x. Ans. x. 6 2 2 4 8. Given a2+x*=b+x+1; to find x. Ans.x 9. Given x+a= a2+x√ b2+x2; to find *. Ans. x 64 2 64 4a 2a 4 -a 2 a. REDUCTION OF TWO, THREE, OR MORE, SIMPLE EQUATIONS, CONTAINING TWO, THREE, OR MORE, UNKNOWN QUANTITIES. PROBLEM I. To exterminate two unknown quantities, or to reduce the twa simple equations containing them to one. : RULE I. 1. Observe which of the unknown quantities is the least involved, and find its value in each of the equations, by the methods already explained. 2. Let the two values thus found be made equal to each other, and there will arise a new equation with only one unknown quantity in it, whose value may be found as before. And consequently ; to find 23-34 x and y. 23-39 2 10+2y 4. Given 4x+y=34, and 4y += 16; to find x and y. 5. Given x and y. 6. Given 2 4 Ans. x8, and y=2. +2= 61 Ans. x, and x+y=s, and x-y=d; to find x and y. 3 sd , and y 25 25 RULE 2. 1. Consider which of the unknown quantities you would first exterminate, and let its value be found in that equation, where it is least involved. 2. Substitute the value thus found for its equal in the other equation, and there will arise a new equation with only one unknown quantity, whose value may be found as before. 1. Given EXAMPLES. {3x+2y=17}; 25 to find x and y. From the first equation x=17-29, And this value, substituted for x in the second, gives 17-2yX3=2, Or 51-6-y-2, or 51-79=2; That is, 7y51-2=49; Whence y=1=7, and x=17-2-17-14-3. 12. Given {+3} ; to find x and y. From the first equation x = 13-у, And this value, being substituted for x in the second, Gives 13-y-y=3, or 13-2y=3; That is, 2y=13-3=10, Or 5, and x=13-y-13-5-8. 3. Given |