Question 1

A sum of money amounting to $\$ 5.80$ consists of dimes and quarters. If there are 28 coins in all, how many are quarters?

Accepted Answer

A)  10 quarters 
B)  25 quarters 
C)  20 quarters 
D)  8 quarters 
A)  10 quarters 
B)  25 quarters 
C)  20 quarters 
D)  8 quarters

Question 2

Solve the system of equations. If the system is inconsistent or has dependent equations, say so.
-$x+3 y+2 z=11$
$4 y+9 z=-12$
$x+7 y+11 z=-11$

Accepted Answer

A)  $\{(0,3,1)\}$ 
B)  $\{(x, y, z) \mid x+3 y+2 z=11\}$; dependent equations 
C)  $\{(7,-1,-1)\}$ 
D)  $\varnothing$; inconsistent system 
A)  $\{(0,3,1)\}$ 
B)  $\{(x, y, z) \mid x+3 y+2 z=11\}$; dependent equations 
C)  $\{(7,-1,-1)\}$ 
D)  $\varnothing$; inconsistent system

Question 3

Solve the system of equations.
-$\frac{6}{x}-\frac{3}{y}=-13$
$\frac{3}{x}+\frac{1}{y}=6$

Accepted Answer

A)  $\left\{\left\{\left(\frac{1}{5}, 3\right)\right\}\right.$ 
B)  $\left\{\left\{\left(\frac{1}{3}, 5\right)\right\}\right.$ 
C)  $\left\{\left\{3, \frac{1}{5}\right)\right\}$ 
D)  $\varnothing$ 
A)  $\left\{\left\{\left(\frac{1}{5}, 3\right)\right\}\right.$ 
B)  $\left\{\left\{\left(\frac{1}{3}, 5\right)\right\}\right.$ 
C)  $\left\{\left\{3, \frac{1}{5}\right)\right\}$ 
D)  $\varnothing$

Question 4

During the 1998-1999 Junior Hockey League season, the Sharks played 64 games. Together, their wins and losses totaled 57 . They tied 15 fewer games than they lost. How many games did they tie that season?

Accepted Answer

A)  5 games 
B)  35 games 
C)  7 games 
D)  22 games 
A)  5 games 
B)  35 games 
C)  7 games 
D)  22 games

Question 5

In solving a system of three equations in three variables, the final step yields the following equation:
$0=0$.
How many solutions does this system have? Explain geometrically.

Accepted Answer

There are an infinite number o

Question 6

A plane flies 500 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is $24 \mathrm{mph}$, what is the speed of the plane in still air?

Accepted Answer

A)  $126 \mathrm{mph}$ 
B)  $136 \mathrm{mph}$ 
C)  $141 \mathrm{mph}$ 
D)  $161 \mathrm{mph}$ 
A)  $126 \mathrm{mph}$ 
B)  $136 \mathrm{mph}$ 
C)  $141 \mathrm{mph}$ 
D)  $161 \mathrm{mph}$

Question 7

The perimeter of a triangle is $66 \mathrm{~cm}$. The triangle is isosceles now, but if its base were lengthened by $6 \mathrm{~cm}$ and each leg were shortened by $3 \mathrm{~cm}$, it would be equilateral. Find the length of the base of the original triangle.

Accepted Answer

A)  $22 \mathrm{~cm}$ 
B)  $25 \mathrm{~cm}$ 
C)  $16 \mathrm{~cm}$ 
D)  $15 \mathrm{~cm}$ 
A)  $22 \mathrm{~cm}$ 
B)  $25 \mathrm{~cm}$ 
C)  $16 \mathrm{~cm}$ 
D)  $15 \mathrm{~cm}$

Question 8

A company manufactures three products. The graph shows the production from 1986 to 1996. During which year did the production of A equal the production of $\mathrm{B}$ ?

Accepted Answer

A)  1996 
B)  600,000 
C)  650,000 
D)  1991 
A)  1996 
B)  600,000 
C)  650,000 
D)  1991

Question 9

Tell how many solutions the system has. Do not actually solve.
-$x+2 y=0$
$y=-\frac{1}{2} x$

Accepted Answer

A)  Infinitely many 
B)  No solution 
C)  One solution 
A)  Infinitely many 
B)  No solution 
C)  One solution

Question 10

There were 600 people at a play. The admission price was $\$ 2$ for adults and $\$ 1$ for children. The admission receipts were $\$ 920$. How many adults and how many children attended?

Accepted Answer

A)  280 adults and 320 children 
B)  320 adults and 280 children 
C)  140 adults and 460 children 
D)  230 adults and 370 children 
A)  280 adults and 320 children 
B)  320 adults and 280 children 
C)  140 adults and 460 children 
D)  230 adults and 370 children

Question 11

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so.
-$x-2 y=-7$
$7 x-3 y=17$

Accepted Answer

A)  $\{(-5,7)\}$ 
B)  $\{(5,6)\}$ 
C)  $\{(4,7)\}$ 
D)  $\varnothing$; inconsistent system 
A)  $\{(-5,7)\}$ 
B)  $\{(5,6)\}$ 
C)  $\{(4,7)\}$ 
D)  $\varnothing$; inconsistent system

Question 12

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
-$x+y=-11$
$\mathrm{y}=-4 \mathrm{x}-5$

Accepted Answer

A)  $\{(2,-13)\}$ 
B)  $\{(1,-11)\}$ 
C)  $\{(-13,2)\}$ 
D)  $\{(3,-20)\}$ 
A)  $\{(2,-13)\}$ 
B)  $\{(1,-11)\}$ 
C)  $\{(-13,2)\}$ 
D)  $\{(3,-20)\}$

Question 13

Tell how many solutions the system has. Do not actually solve.
-$2 x+3 y=6$
$4 x+6 y=12$

Accepted Answer

A)  One solution 
B)  No solution 
C)  Infinitely many 
A)  One solution 
B)  No solution 
C)  Infinitely many

Question 14

$x+y+z=5$
$x-y+5 z=-3$
$5 x+y+z=21$

Accepted Answer

A)  $\{(-1,4,2)\}$ 
B)  $\{(2,-1,4)\}$ 
C)  $\{(-1,2,4)\}$ 
D)  $\{(4,2,-1)\}$ 
A)  $\{(-1,4,2)\}$ 
B)  $\{(2,-1,4)\}$ 
C)  $\{(-1,2,4)\}$ 
D)  $\{(4,2,-1)\}$

Question 15

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
-$5 x+3 y=80$
$2 x+y=30$

Accepted Answer

A)  $\{(0,10)\}$ 
B)  $\{(0,0)\}$ 
C)  $\{(10,10)\}$ 
D)  $\{(10,0)\}$ 
A)  $\{(0,10)\}$ 
B)  $\{(0,0)\}$ 
C)  $\{(10,10)\}$ 
D)  $\{(10,0)\}$

Question 16

A basketball fieldhouse seats 15,000 . Courtside seats sell for $\$ 8$, endzone for $\$ 6$, and balcony for $\$ 4$. The total revenue from a sell-out is $\$ 76,000$. If half the courtside and balcony seats and all the endzone seats are sold, the total revenue is $\$ 44,000$. How many of each type are there?

Accepted Answer

A)  3000 courtside; 3000 endzone; 8,000 balcony 
B)  4000 courtside; 3000 endzone; 8000 balcony 
C)  3200 courtside; 1800 endzone; 10,000 balcony 
D)  3000 courtside; 2000 endzone; 10,000 balcony 
A)  3000 courtside; 3000 endzone; 8,000 balcony 
B)  4000 courtside; 3000 endzone; 8000 balcony 
C)  3200 courtside; 1800 endzone; 10,000 balcony 
D)  3000 courtside; 2000 endzone; 10,000 balcony

Question 17

Andy has 27 coins made up of quarters and half dollars, and their total value is $\$ 9.25$. How many quarters does he have?

Accepted Answer

A)  17 quarters 
B)  12 quarters 
C)  10 quarters 
D)  22 quarters 
A)  17 quarters 
B)  12 quarters 
C)  10 quarters 
D)  22 quarters

Question 18

An express train and a local train both leave Gray's Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.

Accepted Answer

A)  Express: $25 \mathrm{mph}$; local: $12.5 \mathrm{mph}$ 
B)  Express: $50 \mathrm{mph}$; local: $25 \mathrm{mph}$ 
C)  Express: $60 \mathrm{mph}$; local: $30 \mathrm{mph}$ 
D)  Cannot be determined without more information 
A)  Express: $25 \mathrm{mph}$; local: $12.5 \mathrm{mph}$ 
B)  Express: $50 \mathrm{mph}$; local: $25 \mathrm{mph}$ 
C)  Express: $60 \mathrm{mph}$; local: $30 \mathrm{mph}$ 
D)  Cannot be determined without more information

Question 19

Tell how many solutions the system has. Do not actually solve.
-$2 x+5 y=-1$
$4 x+10 y=-2$

Accepted Answer

A)  One solution 
B)  No solution 
C)  Infinitely many 
A)  One solution 
B)  No solution 
C)  Infinitely many

Question 20

Ron and Kathy are ticket-sellers at their class play. Ron is selling student tickets for $\$ 3.00$ each, and Kathy selling adult tickets for $\$ 5.50$ each. If their total income for 19 tickets was $\$ 72.00$, how many tickets did Ron sell?

Accepted Answer

A)  6 tickets 
B)  15 tickets 
C)  11 tickets 
D)  13 tickets 
A)  6 tickets 
B)  15 tickets 
C)  11 tickets 
D)  13 tickets

A sum of money amounting to $\$ 5.80$ consists of dimes and quarters. If there are 28 coins in all, how many are quarters?

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - $x+3 y+2 z=11$ $4 y+9 z=-12$ $x+7 y+11 z=-11$

Solve the system of equations. - $\frac{6}{x}-\frac{3}{y}=-13$ $\frac{3}{x}+\frac{1}{y}=6$

During the 1998-1999 Junior Hockey League season, the Sharks played 64 games. Together, their wins and losses totaled 57 . They tied 15 fewer games than they lost. How many games did they tie that season?

In solving a system of three equations in three variables, the final step yields the following equation: $0=0$ . How many solutions does this system have? Explain geometrically.

A plane flies 500 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is $24 \mathrm{mph}$ , what is the speed of the plane in still air?

The perimeter of a triangle is $66 \mathrm{~cm}$ . The triangle is isosceles now, but if its base were lengthened by $6 \mathrm{~cm}$ and each leg were shortened by $3 \mathrm{~cm}$ , it would be equilateral. Find the length of the base of the original triangle.

Tell how many solutions the system has. Do not actually solve. - $x+2 y=0$ $y=-\frac{1}{2} x$

There were 600 people at a play. The admission price was $\$ 2$ for adults and $\$ 1$ for children. The admission receipts were $\$ 920$ . How many adults and how many children attended?

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $x-2 y=-7$ $7 x-3 y=17$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $x+y=-11$ $\mathrm{y}=-4 \mathrm{x}-5$

Tell how many solutions the system has. Do not actually solve. - $2 x+3 y=6$ $4 x+6 y=12$

$x+y+z=5$ $x-y+5 z=-3$ $5 x+y+z=21$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $5 x+3 y=80$ $2 x+y=30$

Andy has 27 coins made up of quarters and half dollars, and their total value is $\$ 9.25$ . How many quarters does he have?

An express train and a local train both leave Gray's Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.

Tell how many solutions the system has. Do not actually solve. - $2 x+5 y=-1$ $4 x+10 y=-2$

Ron and Kathy are ticket-sellers at their class play. Ron is selling student tickets for $\$ 3.00$ each, and Kathy selling adult tickets for $\$ 5.50$ each. If their total income for 19 tickets was $\$ 72.00$ , how many tickets did Ron sell?

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 4: Systems of Linear Equations

A sum of money amounting to $5.80\$ 5.80$5.80 consists of dimes and quarters. If there are 28 coins in all, how many are quarters?

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - x+3y+2z=11x+3 y+2 z=11x+3y+2z=11 4y+9z=−124 y+9 z=-124y+9z=−12 x+7y+11z=−11x+7 y+11 z=-11x+7y+11z=−11

Solve the system of equations. - 6x−3y=−13\frac{6}{x}-\frac{3}{y}=-13x6​−y3​=−13 3x+1y=6\frac{3}{x}+\frac{1}{y}=6x3​+y1​=6

During the 1998-1999 Junior Hockey League season, the Sharks played 64 games. Together, their wins and losses totaled 57 . They tied 15 fewer games than they lost. How many games did they tie that season?

In solving a system of three equations in three variables, the final step yields the following equation: 0=00=00=0 . How many solutions does this system have? Explain geometrically.

A plane flies 500 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 24mph24 \mathrm{mph}24mph , what is the speed of the plane in still air?

The perimeter of a triangle is 66 cm66 \mathrm{~cm}66 cm . The triangle is isosceles now, but if its base were lengthened by 6 cm6 \mathrm{~cm}6 cm and each leg were shortened by 3 cm3 \mathrm{~cm}3 cm , it would be equilateral. Find the length of the base of the original triangle.

A company manufactures three products. The graph shows the production from 1986 to 1996. During which year did the production of A equal the production of B\mathrm{B}B ?

Tell how many solutions the system has. Do not actually solve. - x+2y=0x+2 y=0x+2y=0 y=−12xy=-\frac{1}{2} xy=−21​x

There were 600 people at a play. The admission price was $2\$ 2$2 for adults and $1\$ 1$1 for children. The admission receipts were $920\$ 920$920 . How many adults and how many children attended?

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - x−2y=−7x-2 y=-7x−2y=−7 7x−3y=177 x-3 y=177x−3y=17

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - x+y=−11x+y=-11x+y=−11 y=−4x−5\mathrm{y}=-4 \mathrm{x}-5y=−4x−5

Tell how many solutions the system has. Do not actually solve. - 2x+3y=62 x+3 y=62x+3y=6 4x+6y=124 x+6 y=124x+6y=12

x+y+z=5x+y+z=5x+y+z=5 x−y+5z=−3x-y+5 z=-3x−y+5z=−3 5x+y+z=215 x+y+z=215x+y+z=21

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - 5x+3y=805 x+3 y=805x+3y=80 2x+y=302 x+y=302x+y=30

Andy has 27 coins made up of quarters and half dollars, and their total value is $9.25\$ 9.25$9.25 . How many quarters does he have?

An express train and a local train both leave Gray's Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.

Tell how many solutions the system has. Do not actually solve. - 2x+5y=−12 x+5 y=-12x+5y=−1 4x+10y=−24 x+10 y=-24x+10y=−2

Ron and Kathy are ticket-sellers at their class play. Ron is selling student tickets for $3.00\$ 3.00$3.00 each, and Kathy selling adult tickets for $5.50\$ 5.50$5.50 each. If their total income for 19 tickets was $72.00\$ 72.00$72.00 , how many tickets did Ron sell?

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

A sum of money amounting to $\$ 5.80$ consists of dimes and quarters. If there are 28 coins in all, how many are quarters?

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - $x+3 y+2 z=11$ $4 y+9 z=-12$ $x+7 y+11 z=-11$

Solve the system of equations. - $\frac{6}{x}-\frac{3}{y}=-13$ $\frac{3}{x}+\frac{1}{y}=6$

In solving a system of three equations in three variables, the final step yields the following equation: $0=0$ . How many solutions does this system have? Explain geometrically.

A plane flies 500 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is $24 \mathrm{mph}$ , what is the speed of the plane in still air?

The perimeter of a triangle is $66 \mathrm{~cm}$ . The triangle is isosceles now, but if its base were lengthened by $6 \mathrm{~cm}$ and each leg were shortened by $3 \mathrm{~cm}$ , it would be equilateral. Find the length of the base of the original triangle.

Tell how many solutions the system has. Do not actually solve. - $x+2 y=0$ $y=-\frac{1}{2} x$

There were 600 people at a play. The admission price was $\$ 2$ for adults and $\$ 1$ for children. The admission receipts were $\$ 920$ . How many adults and how many children attended?

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $x-2 y=-7$ $7 x-3 y=17$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $x+y=-11$ $\mathrm{y}=-4 \mathrm{x}-5$

Tell how many solutions the system has. Do not actually solve. - $2 x+3 y=6$ $4 x+6 y=12$

$x+y+z=5$ $x-y+5 z=-3$ $5 x+y+z=21$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $5 x+3 y=80$ $2 x+y=30$

Andy has 27 coins made up of quarters and half dollars, and their total value is $\$ 9.25$ . How many quarters does he have?

Tell how many solutions the system has. Do not actually solve. - $2 x+5 y=-1$ $4 x+10 y=-2$

Ron and Kathy are ticket-sellers at their class play. Ron is selling student tickets for $\$ 3.00$ each, and Kathy selling adult tickets for $\$ 5.50$ each. If their total income for 19 tickets was $\$ 72.00$ , how many tickets did Ron sell?