## Algebraical Problems, Producing Simple and Quadratic Equations, with Their Solutions; Designed as an Introduction to the Higher Branches of Analytics: to which is Added an Appendix, Containing a Collection of Problems on the Nature and Solution of Equations of Higher Dimensions |

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Page 23

... second by 3 , 4x + by = 46 , and 152 - 6y = 30 ; .. by

... second by 3 , 4x + by = 46 , and 152 - 6y = 30 ; .. by

**addition**, 19≈ = 76 , and x = 4 ; whence , as before , 3y = 23 - 2x Solution of Simple Equations , & c . 23 Solution of Simple Equations, involving three unknown Quan- tities 43. Page 30

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**addition**, and x = 8 ; whence 3y = 100 - 11 100 · - 88 = 12 ; ..y = 4 . 4. Given y + = 7 and + ข = 8 3 2 to find the values of x and y . ( 18. Cor . 1. ) clearing the equations of fractions , by mul- tiplying each by 6 , 3x + 2y = 42 ... Page 31

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**addition**, 50x + 50y = 1050 , and . + y = 21 ; but since x + 49y = 693 , subtracting the upper equation from the lower , 48y = 672 ; ..y = 14 , whence x = 21 y = 21 147 . x + 2 6. Given + 8y = 31 to find the values of x and and y + 5 4 ... Page 32

... 4 , and the preceding one by 3 , 9y + 12x = 144 , and 20y .. by

... 4 , and the preceding one by 3 , 9y + 12x = 144 , and 20y .. by

**addition**, whence 4x = 48 --- 12 x = 88 ; 294 = 232 , and y = 8 , - 3y = 48 and x = 6 . - 24 = 24 , 3x 22 . = 22 7y 9. Given 3x + 2 2x and 32 Solution of Simple Equations. Page 33

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**addition**, 172y = 344 , and y = 2 . Now 6x 44 7y = 44 - 14 = 30 ; .. x = 5 . : 3 - y 41 2 12 2X - = 4 10. Given x + 1 : y and 2X 5 3 to find the values of x and y . From the second equation , ( 18. Cor . 1. ) multiplied by 12 , 8x - 30 ...### Other editions - View all

### Common terms and phrases

a²x² addition answer the conditions arithmetic series arithmetical progression casks common difference completing the square containing cost cube digits distance equal equation a³ equation of fractions extracting the root extracting the square find the values gain geometric series geometrical progression Given 3x Given x² greater guineas harmonic progression least common multiple length less Let 2x Let the number number of days number of gallons number of miles number of shillings number of terms number of yards pence pieces problem proportion px² Quadratics received Required the number second equation sheep shil sold square root squaring both sides Substituting this value subtraction third three numbers Transform the equation transposition travelled unknown quantity values of x wheat whence whole number x²y xy²

### Popular passages

Page 24 - In one of the given equations obtain the value of one of the unknown quantities in terms of the other unknown quantity; Substitute this value in the other equation and solve.

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Page 378 - From two places at a distance of 320 miles, two persons, A and B, set out at the same time to meet each other. A travelled 8 miles a day more than B, and the number of days in which they met was equal to half the number of miles B went in a day. How many miles did each travel, and how far per day ? 20.

Page 2 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.

Page 371 - A detachment of soldiers from a regiment being ordered to march on a particular service, each company furnished four times as many men as there were companies in the...

Page 231 - There are two square buildings, that are paved with stones, a foot square each. The side of one building exceeds that of the other by 12 feet, and both their pavements taken together contain 2120 stones. What are the lengths of them separately 1 Ans.

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Page 375 - A gentleman bought two pieces of silk, which, together, measured 36 yards. Each of them cost as many shillings per yard as there were yards in the piece, and their whole prices were as 4 to 1. What were the lengths of the pieces ? Solution.

Page 365 - There is a cistern, into which water is admitted by three cocks, two of which are of exactly the same dimensions. When they are all open, five-twelfths of the cistern is filled in...

Page 188 - Prob. 3. Find two numbers, the greater of which shall be to the less, as their sum to 42 ; and as their difference to 6.