SIMULTANEOUS EQUATIONS

Exercise 55, problem 1

$ \left\{ \begin{array}{rcrcl} x &+& y &=& 4, \\ 3x &-& 2y &=& 7 . \end{array} \right. $

verified: the printed answer passed a computed check

Exercise 55, problem 10

$ \left\{ \begin{array}{rcrcl} 3x &-& 5y &=& 15, \\ 5x &+& 3y &=& 8 . \end{array} \right. $

verified: the printed answer passed a computed check

Exercise 55, problem 11

$ \left\{ \begin{array}{rcrcl} 3y &-& 2x &=& 3, \\ 4y &-& 6x &=& 2\frac{1}{3} . \end{array} \right. $

verified: the printed answer passed a computed check

Exercise 55, problem 12

$ \left\{ \begin{array}{rcrcl} 3x &+ & 2y &=& 11,\\ 7x &-& 5y &=& 190. \end{array} \right. $

verified: the printed answer passed a computed check

Exercise 55, problem 13

$ \left\{ \begin{array}{rcrcl} \frac{1}{2}x &+& \frac{1}{3}y &=& 11,\\ 8x &+& \frac{2}{5}y &=& 102. \end{array} \right. $

verified: the printed answer passed a computed check

Exercise 55, problem 14

$ \left\{ \begin{array}{rcrcl} 5x &+& 2y &=& 66,\\ \frac{x}{3} &+& \frac{3y}{4} &=& 15\frac{1}{2}. \end{array} \right. $

verified: the printed answer passed a computed check

Exercise 55, problem 15

$\left\{ \begin{matrix}\frac{3x}{5} - \frac{2y}{7} = 35, \\ x + 2y = -63.\end{matrix}\right.$

verified: the printed answer passed a computed check

Exercise 55, problem 16

$\left\{ \begin{matrix}x - \frac{3y}{5} = 6, \\ \frac{2x}{3} + 7y = 189.\end{matrix}\right.$

verified: the printed answer passed a computed check

Exercise 55, problem 17

$\left\{ \begin{matrix}\frac{x + 2y}{3x - y} = 1, \\ \frac{4y - x}{3 + x - 2y} = 2\frac{1}{2}.\end{matrix}\right.$

verified: the printed answer passed a computed check

Exercise 55, problem 18

$\left\{ \begin{matrix}\frac{x + 2y}{x - 2} = -5\frac{2}{3}, \\ \frac{2y - 4x}{3 - y} = -6.\end{matrix}\right.$

verified: the printed answer passed a computed check

Exercise 55, problem 19

$\left\{ \begin{matrix}y - \frac{2y + x}{3} = \frac{2x + y}{4} - 8\frac{3}{4}, \\ \frac{3x + y}{2} - \frac{y}{3} = \frac{109}{10} + \frac{4y - x}{5}.\end{matrix}\right.$

verified: the printed answer passed a computed check

Exercise 55, problem 2

$ \left\{ \begin{array}{rcrcl} x &-& y &=& 2, \\ 2x &+& 5y &=& 18 . \end{array} \right. $

verified: the printed answer passed a computed check

Exercise 55, problem 20

$\left\{ \begin{matrix}x + y = a, \\ x - y = b.\end{matrix}\right.$

verified: the printed answer passed a computed check

Exercise 55, problem 21

$\left\{ \begin{matrix}\frac{3x - 19}{2} + 4 = \frac{3y + x}{3} + \frac{5x - 3}{2}, \\ \frac{4x + 5y}{16} + \frac{2x + y}{2} = \frac{9x - 7}{8} + \frac{3y + 9}{4}.\end{matrix}\right.$

verified: the printed answer passed a computed check

Exercise 55, problem 22

$\left\{ \begin{matrix}\frac{1}{5}(3x - 2y) + \frac{1}{3}(5x - 3y) = x, \\ \frac{4x - 3y}{2} + \frac{2}{3}x - y = 1 + y.\end{matrix}\right.$

verified: the printed answer passed a computed check

Exercise 55, problem 23

If 1 is added to the numerator of a fraction, its value is $\frac{1}{8}$; but if 4 is added to its denominator, its value is $\frac{1}{4}$. What is the fraction?

unverified: no computed check settled this one (yet)

Exercise 55, problem 24

If 2 is subtracted from both numerator and denominator of a certain fraction, its value is $\frac{3}{5}$; and if 1 is added to both numerator and denominator, its value is $\frac{2}{3}$. What is the fraction?

verified: the printed answer passed a computed check

Exercise 55, problem 25

If 2 is added to both numerator and denominator of a certain fraction, its value is $\frac{2}{3}$; but if 3 is subtracted from both numerator and denominator, its value is $\frac{1}{2}$. What is the fraction?

verified: the printed answer passed a computed check

Exercise 55, problem 26

If 3 be subtracted from the numerator of a certain fraction, and 3 be added to the denominator, its value will be $\frac{1}{2}$; but if 5 be added to the numerator, and 5 be subtracted from its denominator, its value will be 2. What is the fraction?

verified: the printed answer passed a computed check

Exercise 55, problem 27

The sum of two numbers divided by 2 is 43, and their difference divided by 2 is 19. What are the numbers?

verified: the printed answer passed a computed check

Exercise 55, problem 28

The sum of two numbers divided by 3 gives as a quotient 30, and their difference divided by 9 gives 4. What are the numbers?

verified: the printed answer passed a computed check

Exercise 55, problem 29

Five years ago the age of a father was four times that of his son; five years hence the age of the father will be $2\frac{1}{3}$ times that of the son. What are their ages?

verified: the printed answer passed a computed check

Exercise 55, problem 3

$ \left\{ \begin{array}{rcrcl} 5x &+& 2y &=& 47, \\ 2x &-& y &=& 8 . \end{array} \right. $

verified: the printed answer passed a computed check

Exercise 55, problem 30

Seven years ago John was one-half as old as Henry, but five years hence he will be three-quarters as old. How old is each?

verified: the printed answer passed a computed check

Exercise 55, problem 31

$A$ and $B$ own herds of cows. If $A$ should sell 6 cows, and $B$ should buy 6, they would have the same number; if $B$ should sell 4 cows to $A$, he would have only half as many as A. How many cows are there in each herd?

verified: the printed answer passed a computed check

Exercise 55, problem 32

The cost of 5 pounds of tea and 7 pounds of coffee is $4.94; the cost of 3 pounds of tea and 6 pounds of coffee is $3.54. What is the cost of the tea and coffee per pound?

verified: the printed answer passed a computed check

Exercise 55, problem 33

What is the price of corn and oats when 4 bushels of corn with 6 bushels of oats cost $4.66, and 5 bushels of corn with 9 bushels of oats cost $6.38?

verified: the printed answer passed a computed check

Exercise 55, problem 34

A merchant mixes tea which cost him 87 cents a pound with tea which cost him 29 cents a pound. The cost of the mixture is $17.98. He sells the mixture at 55 cents a pound and gains $2.92. How many pounds of each did he put into the mixture?

verified: the printed answer passed a computed check

Exercise 55, problem 4

$ \left\{ \begin{array}{rcrcl} 4x &-& 3y &=& 10, \\ 6x &+& 4y &=& 49 . \end{array} \right. $

verified: the printed answer passed a computed check

Exercise 55, problem 5

$ \left\{ \begin{array}{rcrcl} 8x &-& 2y &=& 6, \\ 10x &+& 7y &=& 36 . \end{array} \right. $

verified: the printed answer passed a computed check

Exercise 55, problem 6

$ \left\{ \begin{array}{rcrcl} 2x &-& 5y &=& -11, \\ 3x &+& y &=& 9 . \end{array} \right. $

verified: the printed answer passed a computed check

Exercise 55, problem 7

$ \left\{ \begin{array}{rcrcl} 7x &-& 3y &=& 41, \\ 2x &+& y &=& 12 . \end{array} \right. $

unverified: no computed check settled this one (yet)

Exercise 55, problem 8

$ \left\{ \begin{array}{rcrcl} 2x &+& 9y &=& -5, \\ 11x &+& 15y &=& 7 . \end{array} \right. $

verified: the printed answer passed a computed check

Exercise 55, problem 9

$ \left\{ \begin{array}{rcrcl} 4y &-& 2x &=& 4, \\ 10y &+& 3x &=& -8 . \end{array} \right. $

verified: the printed answer passed a computed check

Exercise 56, problem 1

$5x^2-12 = 33$.

unverified: no computed check settled this one (yet)

Exercise 56, problem 10

$\displaystyle \frac{x+1}{x-1}+\frac{2(x-3)}{x-2} = \frac{16-9x}{x^2-3x+2}$.

unverified: no computed check settled this one (yet)

Exercise 56, problem 11

$\displaystyle \frac{1}{(2-x)(3-x)}-\frac{2}{(1-x)(x-3)}+\frac{1}{(x-1)(x-2)} = \frac{1}{2-x}+\frac{1}{(x-1)(2-x)(x-3)}$.

unverified: no computed check settled this one (yet)

Exercise 56, problem 12

$\displaystyle \frac{1}{6x+6}-\frac{1}{2x+2}+\frac{10}{3-3x^2} = \frac{x}{3(1-x)}$.

unverified: no computed check settled this one (yet)

Exercise 56, problem 13

A father is 30 years old, and his son is two years old. In how many years will the father be three times as old as his son?

verified: the printed answer passed a computed check

3 ENTER 2 × 30 −

1 ENTER 3 −

÷

Exercise 56, problem 14

Divide the number 112 into two parts such that the smaller divided by their difference will give as a quotient 3.

verified: the printed answer passed a computed check

Exercise 56, problem 15

The numerator of a fraction is 4 less than the denominator; if 30 be added to the denominator, or if 10 be subtracted from the numerator, the resulting fractions will be equal. What is the original fraction?

verified: the printed answer passed a computed check

Exercise 56, problem 2

$3x^2+4 = 16$.

unverified: no computed check settled this one (yet)

Exercise 56, problem 3

$4x^2+ll = 136-x^2$.

unverified: no computed check settled this one (yet)

Exercise 56, problem 4

$5(3x^2-1) = 11(x^2+1)$.

unverified: no computed check settled this one (yet)

Exercise 56, problem 5

$\displaystyle \frac{2}{5x^2}-\frac{1}{3x^2} = \frac{4}{15}$.

unverified: no computed check settled this one (yet)

Exercise 56, problem 6

$\displaystyle \frac{x^2-1}{6}+\frac{1}{4} = \frac{x^2+1}{8}$.

unverified: no computed check settled this one (yet)

Exercise 56, problem 7

$(x+3)^2 = 6x+58$.

unverified: no computed check settled this one (yet)

Exercise 56, problem 8

$\displaystyle 6x+2+\frac{16}{x} = \frac{15+40x}{4}-1\frac{3}{4}$.

unverified: no computed check settled this one (yet)

Exercise 56, problem 9

$\displaystyle \frac{x-3}{x-1}+\frac{x+1}{x+3}+\frac{8}{x^2+2x-3} = 0$.

unverified: no computed check settled this one (yet)

Exercise 57, problem 1

$x^{2}+3x=18$.

verified: the printed answer passed a computed check

Exercise 57, problem 10

$adx-acx^{2}=bcx-bd$.

verified: the printed answer passed a computed check

Exercise 57, problem 11

$(x+3)(x-3)=8(x+3)$.

verified: the printed answer passed a computed check

Exercise 57, problem 12

$(x+2)(x-5)=4(x-4)$.

verified: the printed answer passed a computed check

Exercise 57, problem 13

$\displaystyle \frac{x}{5}+\frac{2}{x}=1\frac{2}{5}$.

verified: the printed answer passed a computed check

Exercise 57, problem 14

$\displaystyle \frac{x}{3}-2=\frac{x^{2}}{12}-\frac{x}{2}$.

verified: the printed answer passed a computed check

Exercise 57, problem 15

$\displaystyle \frac{8}{x-2}-3+\frac{x+1}{7}=0$.

verified: the printed answer passed a computed check

Exercise 57, problem 16

$\displaystyle \frac{x}{x+1}-2\frac{1}{6}+\frac{x+1}{x}=0$.

verified: the printed answer passed a computed check

Exercise 57, problem 17

$\displaystyle x+4=3x-\frac{24}{x-1}$.

verified: the printed answer passed a computed check

Exercise 57, problem 18

$\displaystyle \frac{x-1}{x+1}+\frac{x+3}{x-3}=\frac{2(x+2)}{x-2}$.

verified: the printed answer passed a computed check

Exercise 57, problem 19

$\displaystyle \frac{x-1}{x+2}-\frac{3x^{2}+2}{x^{2}-4}=\frac{3x}{2-x}$.

verified: the printed answer passed a computed check

Exercise 57, problem 2

$x^{2}+5x=14$.

verified: the printed answer passed a computed check

Exercise 57, problem 20

$\displaystyle \frac{2x}{3-x}+\frac{2x(x-3)}{x^2-9}=\frac{x-3}{x+3}$.

unverified: no computed check settled this one (yet)

Exercise 57, problem 21

At what time between 4 and 5 o’clock are the hands of a clock opposite each other?

verified: the printed answer passed a computed check

120 ENTER 180 +

ENTER 6 ENTER 1 ENTER 2 ÷ − ÷

Exercise 57, problem 22

John, having three times as much money as Lewis, gave Lewis $2, and then had twice as much as Lewis. How much had each at first?

verified: the printed answer passed a computed check

Exercise 57, problem 23

A fish is 3 feet long; its head is equal in length to the tail, and its body is five times the length of the head and tail together. What is the length of the head?

verified: the printed answer passed a computed check

3 ENTER 12 ×

12 ÷

Exercise 57, problem 24

In how many days can A, B, and C build a boat if they work together, provided A alone can build it in 24 days, B in 18 days, and C in 30 days?

verified: the printed answer passed a computed check

Exercise 57, problem 3

$x(x-1)=72$.

verified: the printed answer passed a computed check

Exercise 57, problem 4

$x^{2}=10x-21$.

verified: the printed answer passed a computed check

Exercise 57, problem 5

$23x=120+x^{2}$.

verified: the printed answer passed a computed check

Exercise 57, problem 6

$187=x^{2}+6x$.

verified: the printed answer passed a computed check

Exercise 57, problem 7

$x^{2}-2bx=-b^{2}$.

verified: the printed answer passed a computed check

Exercise 57, problem 8

$x^{2}=4ax-3a^{2}$.

verified: the printed answer passed a computed check

Exercise 57, problem 9

$x^{2}+(a-1)x=a$.

verified: the printed answer passed a computed check

Exercise 58, problem 1

When $a=l$, $b = 3$, $c = 5$, and $d = O$, what is the value of $\displaystyle \frac{4a+b^2+b^2c^2+ad}{b^2+c^2+d^2}-\frac{1+a^2c^2}{a^2+c^2+d^2} +\frac{a^2+b^2+d^2}{1+a^2b^2+bd}-\frac{a^2+2ab+b^2}{b^2-2bc+c^2}$?

verified: the printed answer passed a computed check

Exercise 58, problem 10

Simplify (1x-1-3(x+3)(x-1))÷(1x+3+1(x-1)(x+3)).

verified: the printed answer passed a computed check

Exercise 58, problem 2

Prove that $\displaystyle (x^{2}+xy+y^{2})(x^{2}-xy+y^2)=\frac{x^{6}-y^{6}}{x^{2}-y^{2}}$

unverified: no computed check settled this one (yet)

Exercise 58, problem 3

Solve $(x+5)^{2}-(x+1)^{2}-16x=(x-1)^{2}-(x-5)^{2}$.

verified: the printed answer passed a computed check

5 ENTER 2 × 1 ENTER 2 × − 16 −

1 ENTER 2 × +/− 5 ENTER 2 × + −

1 ENTER 5 GOLD x² − 5 GOLD x² − 1 GOLD x² +

x↔y ÷

Exercise 58, problem 4

A tank is filled by two pipes, $A$ and $B$, running together, in 12 hours, and by the pipe $B$ alone in 20 hours. In what time will the pipe $A$ alone fill it?

verified: the printed answer passed a computed check

12 1/x 20 1/x −

1/x

Exercise 58, problem 5

Find the G.C.F. of $x^{3}+1-x-x^{2}$, $x^{3}+x-1-x^{2}$, $x^{4}-1$, and $x^{2}-4x+3$.

verified: the printed answer passed a computed check

Exercise 58, problem 6

Divide $a^{5}+a^{4}b-a^{3}b^{2}+a^{3}-2ab^{2}+b^{3}$ by $a^{3}-b+a$.

verified: the printed answer passed a computed check

Exercise 58, problem 7

Find the square root of $5y^{4}+1+12y^{5}-2y-2y^{3}+4y^{6}+7y^{2}$.

unverified: no computed check settled this one (yet)

Exercise 58, problem 8

Expand (x+1)(x+2)-(2x+1)(2x+3)+(x-4)(x-9)+(x-5)^2.

verified: the printed answer passed a computed check

Exercise 58, problem 9

Solve $\displaystyle \frac{x+2}{x-2}+\frac{x-2}{x+2}=\frac{5}{2}$.

verified: the printed answer passed a computed check