Question 1

$x-y+2 z=5$
$4 \mathrm{x}+\mathrm{z}=0$
$x+3 y+z=-15$

Accepted Answer

A)  $\{(0,0,-5)\}$ 
B)  $\{(0,-5,0)\}$ 
C)  $\{(0,-5,5)\}$ 
D)  $\{(-5,0,-5)\}$ 
A)  $\{(0,0,-5)\}$ 
B)  $\{(0,-5,0)\}$ 
C)  $\{(0,-5,5)\}$ 
D)  $\{(-5,0,-5)\}$ B

Question 2

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response
-What is indicated by the occurrence of a false statement such as " $0=1$ " when you solve a system of two linear equation (in two variables) using substitution?

Accepted Answer

The system is inconsistent.

Question 3

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
-$x-y=4$
$x+y=12$

Accepted Answer

A)  $\{(4,8)\}$ 
B)  $\{(8,4)\}$ 
C)  $\{(8,16)\}$ 
D)  $\{(16,8)\}$ 
A)  $\{(4,8)\}$ 
B)  $\{(8,4)\}$ 
C)  $\{(8,16)\}$ 
D)  $\{(16,8)\}$ B

Question 4

The table shown was generated by a graphing calculator. The functions defined by $y_{1}$ and y2 are linear. Based on the table, find the equation for $\mathrm{y} 1$.

Accepted Answer

A)  $y_{1}=-x+9$ 
B)  $y_{1}=2 x+9$ 
C)  $y_{1}=-x+3$ 
D)  $\mathrm{y}_{1}=2 \mathrm{x}+3$ 
A)  $y_{1}=-x+9$ 
B)  $y_{1}=2 x+9$ 
C)  $y_{1}=-x+3$ 
D)  $\mathrm{y}_{1}=2 \mathrm{x}+3$

Question 5

Jill is $12 \mathrm{~km}$ away from Joe. Both begin to walk toward each other at the same time. Jill walks at $1.5 \mathrm{~km}$ per hour. If they meet in 3 hours, how fast is Joe walking?

Accepted Answer

A)  $1.5 \mathrm{~km}$ per hour 
B)  $3.5 \mathrm{~km}$ per hour 
C)  $4.5 \mathrm{~km}$ per hour 
D)  $2.5 \mathrm{~km}$ per hour 
A)  $1.5 \mathrm{~km}$ per hour 
B)  $3.5 \mathrm{~km}$ per hour 
C)  $4.5 \mathrm{~km}$ per hour 
D)  $2.5 \mathrm{~km}$ per hour

Question 6

Solve the problem using a system of equations.
-A company sells nuts in bulk quantities. When bought in bulk, peanuts sell for $\$ 1.20$ per pound, almonds for $\$ 2.35$ per pound, and cashews for $\$ 3.30$ per pound. Suppose a specialty shop wants a mixture of 210 pounds that will cost $\$ 2.42$ per pound. Find the number of pounds of each type of nut if the sum of the number of pounds of almonds and cashews is twice the number of pounds of peanuts. Round your answers to the nearest pound.

Accepted Answer

A)  Peanuts: $70 \mathrm{lb}$., almonds: $40 \mathrm{lb}$., cashews: $100 \mathrm{lb}$. 
B)  Peanuts: $40 \mathrm{lb}$., almonds: $100 \mathrm{lb}$., cashews: $70 \mathrm{lb}$. 
C)  Peanuts: $80 \mathrm{lb}$., almonds: $40 \mathrm{lb} .$, cashews: $90 \mathrm{lb}$. 
D)  Peanuts: $100 \mathrm{lb}$., almonds: 70 lb., cashews: $40 \mathrm{lb}$. 
A)  Peanuts: $70 \mathrm{lb}$., almonds: $40 \mathrm{lb}$., cashews: $100 \mathrm{lb}$. 
B)  Peanuts: $40 \mathrm{lb}$., almonds: $100 \mathrm{lb}$., cashews: $70 \mathrm{lb}$. 
C)  Peanuts: $80 \mathrm{lb}$., almonds: $40 \mathrm{lb} .$, cashews: $90 \mathrm{lb}$. 
D)  Peanuts: $100 \mathrm{lb}$., almonds: 70 lb., cashews: $40 \mathrm{lb}$.

Question 7

After retirement, Kelly's company offers her two options for receiving her retirement pension. According the the first plan, she will receive monthly payments from a variable annuity that initially pays $\$ 700$ per month then decreases each month at a rate of $\$ 25$ per month per year. Optionally, she may choose a plan that pays her a fixed amount of $\$ 500$ per month for the rest of her life. The monthly payments for the two plans are illustrated in the graph below. If Kelly's remaining life expectancy is 20 years, which plan would be the better choice?

Accepted Answer

A)  The fixed annuity 
B)  The variable annuity 
C)  Both plans are equally attractive. 
A)  The fixed annuity 
B)  The variable annuity 
C)  Both plans are equally attractive.

Question 8

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
-$x=y-6$
$7 x=4 y$

Accepted Answer

A)  $\{(-8,2)\}$ 
B)  $\{(8,14)\}$ 
C)  $\{(0,0)\}$ 
D)  $\{(14,8)\}$ 
A)  $\{(-8,2)\}$ 
B)  $\{(8,14)\}$ 
C)  $\{(0,0)\}$ 
D)  $\{(14,8)\}$

Question 9

Tell how many solutions the system has. Do not actually solve.
-$4 x-16 y=12$
$y=\frac{1}{4} x-\frac{3}{4}$

Accepted Answer

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

Question 10

A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels $5 \mathrm{mph}$ slower than the power boat. Find the speed of each boat.

Accepted Answer

A)  Power boat: $15 \mathrm{mph}$; cabin cruiser: $10 \mathrm{mph}$ 
B)  Power boat: $20 \mathrm{mph}$; cabin cruiser: $15 \mathrm{mph}$ 
C)  Power boat: $10 \mathrm{mph}$; cabin cruiser: $5 \mathrm{mph}$ 
D)  Cannot be determined without more information 
A)  Power boat: $15 \mathrm{mph}$; cabin cruiser: $10 \mathrm{mph}$ 
B)  Power boat: $20 \mathrm{mph}$; cabin cruiser: $15 \mathrm{mph}$ 
C)  Power boat: $10 \mathrm{mph}$; cabin cruiser: $5 \mathrm{mph}$ 
D)  Cannot be determined without more information

Question 11

John and Tony start from Grays lake at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find how fast each walks.

Accepted Answer

A)  Tony: $3 \mathrm{mph}$; John: $6 \mathrm{mph}$ 
B)  Tony: $\frac{5}{3} \mathrm{mph}$; John: $\frac{10}{3} \mathrm{mph}$ 
C)  Tony: $\frac{3}{5} \mathrm{mph}$; John: $\frac{6}{5} \mathrm{mph}$ 
D)  Cannot be determined without more information 
A)  Tony: $3 \mathrm{mph}$; John: $6 \mathrm{mph}$ 
B)  Tony: $\frac{5}{3} \mathrm{mph}$; John: $\frac{10}{3} \mathrm{mph}$ 
C)  Tony: $\frac{3}{5} \mathrm{mph}$; John: $\frac{6}{5} \mathrm{mph}$ 
D)  Cannot be determined without more information

Question 12

Solve the system of equations. If the system is inconsistent or has dependent equations, say so.
-$x-y+8 z=-107$
$x+2 y=21$
$2 \mathrm{x}+\mathrm{y}+8 \mathrm{z}=-80$

Accepted Answer

A)  $\varnothing$; inconsistent system 
B)  $\{(5,8,0)\}$ 
C)  $\{(x, y, z) \mid 2 x+y+8 z=-80\}$; dependent equations 
D)  $\{(5,8,-13)\}$ 
A)  $\varnothing$; inconsistent system 
B)  $\{(5,8,0)\}$ 
C)  $\{(x, y, z) \mid 2 x+y+8 z=-80\}$; dependent equations 
D)  $\{(5,8,-13)\}$

Question 13

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.
-$8 x+6 y=24$
$-3 x+2 y=8$

Accepted Answer

A)  $\{(-1,5)\}$ 
B)  $\{(0,4)\}$ 
C)  $\{(0,5)\}$ 
D)  $\varnothing$; inconsistent system 
A)  $\{(-1,5)\}$ 
B)  $\{(0,4)\}$ 
C)  $\{(0,5)\}$ 
D)  $\varnothing$; inconsistent system

Question 14

Which of the ordered pairs is the only possible solution for the system whose graphs are shown in the viewing window of a graphing calculator?

Accepted Answer

A)  $(8,-30)$ 
B)  $(-22,0)$ 
C)  $(0,-22)$ 
D)  $(-8,-30)$ 
A)  $(8,-30)$ 
B)  $(-22,0)$ 
C)  $(0,-22)$ 
D)  $(-8,-30)$

Question 15

During the 1998-1999 Junior Hockey League season, the Sharks played 57 games. Together, their wins and losses totaled 51 . They tied 14 fewer games than they lost. How many games did they win that season?

Accepted Answer

A)  6 games 
B)  20 games 
C)  27 games 
D)  31 games 
A)  6 games 
B)  20 games 
C)  27 games 
D)  31 games

Question 16

Solve by any method. Assume $a$ and $b$ represent nonzero constants.
-$4 a x+3 y=1$
$y=2 a x$

Accepted Answer

A)  $\left\{\left(\frac{1}{10 a}, \frac{1}{5}\right)\right\}$ 
B)  $\left\{\left\{\left(\frac{1}{5}, \frac{1}{10 a}\right)\right\}\right.$ 
C)  $\left\{\left(\frac{\mathrm{a}}{10}, \frac{1}{5}\right)\right\}$ 
D)  $\left\{\left(\frac{1}{10}, \frac{1}{5}\right)\right\}$ 
A)  $\left\{\left(\frac{1}{10 a}, \frac{1}{5}\right)\right\}$ 
B)  $\left\{\left\{\left(\frac{1}{5}, \frac{1}{10 a}\right)\right\}\right.$ 
C)  $\left\{\left(\frac{\mathrm{a}}{10}, \frac{1}{5}\right)\right\}$ 
D)  $\left\{\left(\frac{1}{10}, \frac{1}{5}\right)\right\}$

Question 17

Which of the ordered pairs listed is the only possible solution for the system whose graphs are shown in the viewing window of a graphing calculator?

Accepted Answer

A)  $(-16,-7)$ 
B)  $(16,-7)$ 
C)  $(-20,12)$ or $(16,7)$ 
D)  None of the above 
A)  $(-16,-7)$ 
B)  $(16,-7)$ 
C)  $(-20,12)$ or $(16,7)$ 
D)  None of the above

Question 18

Michael's bank contains only nickels, dimes, and quarters. There are 58 coins in all, valued at $\$ 5.05$. The number of nickels is 6 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

Accepted Answer

A)  9 
B)  12 
C)  42 
D)  7 
A)  9 
B)  12 
C)  42 
D)  7

Question 19

$3 x-y=12$
$2 y+z=13$
$x+4 z=33$

Accepted Answer

A)  $\{(5,3,-7)\}$ 
B)  $\{(10,6,14)\}$ 
C)  $\{(5,3,7)\}$ 
D)  $\{(-5,-3,-7)\}$ 
A)  $\{(5,3,-7)\}$ 
B)  $\{(10,6,14)\}$ 
C)  $\{(5,3,7)\}$ 
D)  $\{(-5,-3,-7)\}$

Question 20

Solve the system. Express the solution in the form $(x, y, z, w)$.
-$5 x+y-3 z+w=-20$
$\begin{aligned}-x+5 y+z-5 w & =20 \ 3 x-y+5 z+3 w & =20 \ x+y-5 z-w & =-26\end{aligned}$

Accepted Answer

A)  $\{(-2,0,7,1)\}$ 
B)  $\{(-1,-6,12,5)\}$ 
C)  $\{(1,-2,6,-5)\}$ 
D)  $\{(1,-4,0,5)\}$ 
A)  $\{(-2,0,7,1)\}$ 
B)  $\{(-1,-6,12,5)\}$ 
C)  $\{(1,-2,6,-5)\}$ 
D)  $\{(1,-4,0,5)\}$

$x-y+2 z=5$ $4 \mathrm{x}+\mathrm{z}=0$ $x+3 y+z=-15$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response -What is indicated by the occurrence of a false statement such as " $0=1$ " when you solve a system of two linear equation (in two variables) using substitution?

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $x-y=4$ $x+y=12$

Jill is $12 \mathrm{~km}$ away from Joe. Both begin to walk toward each other at the same time. Jill walks at $1.5 \mathrm{~km}$ per hour. If they meet in 3 hours, how fast is Joe walking?

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $x=y-6$ $7 x=4 y$

Tell how many solutions the system has. Do not actually solve. - $4 x-16 y=12$ $y=\frac{1}{4} x-\frac{3}{4}$

A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels $5 \mathrm{mph}$ slower than the power boat. Find the speed of each boat.

John and Tony start from Grays lake at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find how fast each walks.

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - $x-y+8 z=-107$ $x+2 y=21$ $2 \mathrm{x}+\mathrm{y}+8 \mathrm{z}=-80$

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $8 x+6 y=24$ $-3 x+2 y=8$

Which of the ordered pairs is the only possible solution for the system whose graphs are shown in the viewing window of a graphing calculator?

During the 1998-1999 Junior Hockey League season, the Sharks played 57 games. Together, their wins and losses totaled 51 . They tied 14 fewer games than they lost. How many games did they win that season?

Solve by any method. Assume $a$ and $b$ represent nonzero constants. - $4 a x+3 y=1$ $y=2 a x$

Which of the ordered pairs listed is the only possible solution for the system whose graphs are shown in the viewing window of a graphing calculator?

Michael's bank contains only nickels, dimes, and quarters. There are 58 coins in all, valued at $\$ 5.05$ . The number of nickels is 6 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

$3 x-y=12$ $2 y+z=13$ $x+4 z=33$

Solve the system. Express the solution in the form $(x, y, z, w)$ . - $5 x+y-3 z+w=-20$ -x+5y+z-5w =20 3x-y+5z+3w =20 x+y-5z-w =-26

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

x−y+2z=5x-y+2 z=5x−y+2z=5 4x+z=04 \mathrm{x}+\mathrm{z}=04x+z=0 x+3y+z=−15x+3 y+z=-15x+3y+z=−15

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response -What is indicated by the occurrence of a false statement such as " 0=10=10=1 " when you solve a system of two linear equation (in two variables) using substitution?

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - x−y=4x-y=4x−y=4 x+y=12x+y=12x+y=12

The table shown was generated by a graphing calculator. The functions defined by y1y_{1}y1​ and y2 are linear. Based on the table, find the equation for y1\mathrm{y} 1y1 .

Jill is 12 km12 \mathrm{~km}12 km away from Joe. Both begin to walk toward each other at the same time. Jill walks at 1.5 km1.5 \mathrm{~km}1.5 km per hour. If they meet in 3 hours, how fast is Joe walking?

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - x=y−6x=y-6x=y−6 7x=4y7 x=4 y7x=4y

Tell how many solutions the system has. Do not actually solve. - 4x−16y=124 x-16 y=124x−16y=12 y=14x−34y=\frac{1}{4} x-\frac{3}{4}y=41​x−43​

A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels 5mph5 \mathrm{mph}5mph slower than the power boat. Find the speed of each boat.

John and Tony start from Grays lake at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find how fast each walks.

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - x−y+8z=−107x-y+8 z=-107x−y+8z=−107 x+2y=21x+2 y=21x+2y=21 2x+y+8z=−802 \mathrm{x}+\mathrm{y}+8 \mathrm{z}=-802x+y+8z=−80

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - 8x+6y=248 x+6 y=248x+6y=24 −3x+2y=8-3 x+2 y=8−3x+2y=8

Which of the ordered pairs is the only possible solution for the system whose graphs are shown in the viewing window of a graphing calculator?

During the 1998-1999 Junior Hockey League season, the Sharks played 57 games. Together, their wins and losses totaled 51 . They tied 14 fewer games than they lost. How many games did they win that season?

Solve by any method. Assume aaa and bbb represent nonzero constants. - 4ax+3y=14 a x+3 y=14ax+3y=1 y=2axy=2 a xy=2ax

Which of the ordered pairs listed is the only possible solution for the system whose graphs are shown in the viewing window of a graphing calculator?

Michael's bank contains only nickels, dimes, and quarters. There are 58 coins in all, valued at $5.05\$ 5.05$5.05 . The number of nickels is 6 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

3x−y=123 x-y=123x−y=12 2y+z=132 y+z=132y+z=13 x+4z=33x+4 z=33x+4z=33

Solve the system. Express the solution in the form (x,y,z,w)(x, y, z, w)(x,y,z,w) . - 5x+y−3z+w=−205 x+y-3 z+w=-205x+y−3z+w=−20 -x+5y+z-5w =20 3x-y+5z+3w =20 x+y-5z-w =-26

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

$x-y+2 z=5$ $4 \mathrm{x}+\mathrm{z}=0$ $x+3 y+z=-15$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response -What is indicated by the occurrence of a false statement such as " $0=1$ " when you solve a system of two linear equation (in two variables) using substitution?

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $x-y=4$ $x+y=12$

Jill is $12 \mathrm{~km}$ away from Joe. Both begin to walk toward each other at the same time. Jill walks at $1.5 \mathrm{~km}$ per hour. If they meet in 3 hours, how fast is Joe walking?

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $x=y-6$ $7 x=4 y$

Tell how many solutions the system has. Do not actually solve. - $4 x-16 y=12$ $y=\frac{1}{4} x-\frac{3}{4}$

A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels $5 \mathrm{mph}$ slower than the power boat. Find the speed of each boat.

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - $x-y+8 z=-107$ $x+2 y=21$ $2 \mathrm{x}+\mathrm{y}+8 \mathrm{z}=-80$

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $8 x+6 y=24$ $-3 x+2 y=8$

Solve by any method. Assume $a$ and $b$ represent nonzero constants. - $4 a x+3 y=1$ $y=2 a x$

Michael's bank contains only nickels, dimes, and quarters. There are 58 coins in all, valued at $\$ 5.05$ . The number of nickels is 6 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

$3 x-y=12$ $2 y+z=13$ $x+4 z=33$

Solve the system. Express the solution in the form $(x, y, z, w)$ . - $5 x+y-3 z+w=-20$ -x+5y+z-5w =20 3x-y+5z+3w =20 x+y-5z-w =-26