Question 1

$7 \mathrm{x}-\mathrm{y}-4 \mathrm{z}=19$
$3 x-8 z=-4$
$7 \mathrm{y}+\mathrm{z}=9$

Accepted Answer

A)  $\{(-4,1,8)\}$ 
B)  $\{(4,1,2)\}$ 
C)  $\{(4,2,1)\}$ 
D)  $\{(-4,8,1)\}$ 
A)  $\{(-4,1,8)\}$ 
B)  $\{(4,1,2)\}$ 
C)  $\{(4,2,1)\}$ 
D)  $\{(-4,8,1)\}$

Question 2

During the 1998-1999 Little League season, the Tigers played 51 games. They lost 15 more games than they won. How many games did they win that season?

Accepted Answer

A)  16 games 
B)  19 games 
C)  18 games 
D)  17 games 
A)  16 games 
B)  19 games 
C)  18 games 
D)  17 games

Question 3

In solving a system of three equations in three variables, the final step yields the following equation: $0=-1$
How many solutions does this system have? Explain geometrically.

Accepted Answer

There are no solutions. All th

Question 4

$5 x+2 y+z=-11$
$2 x-3 y-z=17$
$7 \mathrm{x}+\mathrm{y}+2 \mathrm{z}=-4$

Accepted Answer

A)  $\{(3,0,-4)\}$ 
B)  $\{(0,6,-1)\}$ 
C)  $\{(-3,0,4)\}$ 
D)  $\{(0,-6,1)\}$ 
A)  $\{(3,0,-4)\}$ 
B)  $\{(0,6,-1)\}$ 
C)  $\{(-3,0,4)\}$ 
D)  $\{(0,-6,1)\}$

Question 5

Tell how many solutions the system has. Do not actually solve.
-$x-3 y=6$
$3 y+1=x$

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
-$8 y-8=-x$
$2 x-5 y=-5$

Accepted Answer

A)  $\{(1,1)\}$ 
B)  $\{(0,0)\}$ 
C)  $\{(1,0)\}$ 
D)  $\{(0,1)\}$ 
A)  $\{(1,1)\}$ 
B)  $\{(0,0)\}$ 
C)  $\{(1,0)\}$ 
D)  $\{(0,1)\}$

Question 8

$4 x-3 z=10$
$3 y+4 z=-9$
$\frac{1}{4} x+\frac{2}{3} y=-2$

Accepted Answer

A)  $\left\{\left\{-\frac{64}{5},-\frac{423}{101}, \frac{90}{101}\right)\right\}$ 
B)  $\left\{\left(\left\{\frac{320}{101},-\frac{423}{101}, \frac{90}{101}\right)\right\}\right.$ 
C)  $\left\{\left\{-\frac{320}{101}, \frac{423}{101},-\frac{90}{101}\right)\right\}$ 
D)  $\left\{\left\{-\frac{320}{283}, \frac{117}{31},-\frac{90}{283}\right)\right\}$ 
A)  $\left\{\left\{-\frac{64}{5},-\frac{423}{101}, \frac{90}{101}\right)\right\}$ 
B)  $\left\{\left(\left\{\frac{320}{101},-\frac{423}{101}, \frac{90}{101}\right)\right\}\right.$ 
C)  $\left\{\left\{-\frac{320}{101}, \frac{423}{101},-\frac{90}{101}\right)\right\}$ 
D)  $\left\{\left\{-\frac{320}{283}, \frac{117}{31},-\frac{90}{283}\right)\right\}$

Question 9

The speed of a stream is $6 \mathrm{mph}$. If a boat travels 54 miles downstream in the same time that it takes to travel 27 miles upstream, what is the speed of the boat in still water?

Accepted Answer

A)  $18 \mathrm{mph}$ 
B)  $20 \mathrm{mph}$ 
C)  $12 \mathrm{mph}$ 
D)  $21 \mathrm{mph}$ 
A)  $18 \mathrm{mph}$ 
B)  $20 \mathrm{mph}$ 
C)  $12 \mathrm{mph}$ 
D)  $21 \mathrm{mph}$

Question 10

Candy and Delvis are riding bicycles in the same direction. Candy rides at a speed of 3 miles per hour, and Delvis rides at a speed of 9 miles per hour. If they started at the same place (and at the same time), then after 5 hours what is the distance between them?

Accepted Answer

A)  39 miles 
B)  27 miles 
C)  31 miles 
D)  30 miles 
A)  39 miles 
B)  27 miles 
C)  31 miles 
D)  30 miles

Question 11

During the 1998-1999 Junior Hockey League season, the Sharks played 44 games. Together, their wins and losses totaled 40 . They tied 8 fewer games than they lost. How many games did they lose that season?

Accepted Answer

A)  12 games 
B)  28 games 
C)  10 games 
D)  4 games 
A)  12 games 
B)  28 games 
C)  10 games 
D)  4 games

Question 12

Solving for which variable in which equation involves the least amount of work?
$7 x=42$
$x-8 y=78$

Accepted Answer

A)  $\mathrm{x}$ in equation 1 
B)  y in equation 1 
C)  $x$ in equation 2 
D)  y in equation 2 
A)  $\mathrm{x}$ in equation 1 
B)  y in equation 1 
C)  $x$ in equation 2 
D)  y in equation 2

Question 13

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.
-$x-4 y=-4$
$-4 x-3 y=-3$

Accepted Answer

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

Question 14

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so.
-$3 x+4 y+z=18$
$2 \mathrm{x}-4 \mathrm{y}-\mathrm{z}=-3$
$4 \mathrm{x}+\mathrm{y}+5 \mathrm{z}=19$

Accepted Answer

A)  $\{(3,1,2)\}$ 
B)  $\{(1,2,3)\}$ 
C)  $\{(3,2,1)\}$ 
D)  $\varnothing$; inconsistent system 
A)  $\{(3,1,2)\}$ 
B)  $\{(1,2,3)\}$ 
C)  $\{(3,2,1)\}$ 
D)  $\varnothing$; inconsistent system

Question 15

Betsy doesn't trust banks, so her savings are hidden under her mattress. Alla has her savings in an investment at simple interest. During which years would Betsy's savings be more than Alla's?

Accepted Answer

A)  $1989-1996$ 
B)  1989 
C)  $1986-1988$ 
D)  1986 - 1989 
A)  $1989-1996$ 
B)  1989 
C)  $1986-1988$ 
D)  1986 - 1989

Question 16

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
-$x=22-4 y$
$5 x+3 y=8$

Accepted Answer

A)  $\{(2,7)\}$ 
B)  $\varnothing$; inconsistent system 
C)  $\{(-3,7)\}$ 
D)  $\{(-2,6)\}$ 
A)  $\{(2,7)\}$ 
B)  $\varnothing$; inconsistent system 
C)  $\{(-3,7)\}$ 
D)  $\{(-2,6)\}$

Question 17

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
-$y=1.5 x$
$0)5 \mathrm{x}+1.8 \mathrm{y}=6.4$

Accepted Answer

A)  $\{(3,2)\}$ 
B)  $\{(2,-3)\}$ 
C)  $\{(2,3)\}$ 
D)  $\{(-2,3)\}$ 
A)  $\{(3,2)\}$ 
B)  $\{(2,-3)\}$ 
C)  $\{(2,3)\}$ 
D)  $\{(-2,3)\}$

Question 18

Solve the system of equations. If the system is inconsistent or has dependent equations, say so.
-$\begin{array}{l}
2 x+10 y+10 z=30 \
x+5 y+5 z=-10 \
x+y+z=-3
\end{array}$

Accepted Answer

A)  $ \{(x, y, z) \mid x+5 y+5 z=-10\} $; dependent equations 
B)  $ \{(-3,2,1)\} $ 
C)  $ \{(2,1,-3)\} $ 
D)  $ \varnothing $; inconsistent system 
A)  $ \{(x, y, z) \mid x+5 y+5 z=-10\} $; dependent equations 
B)  $ \{(-3,2,1)\} $ 
C)  $ \{(2,1,-3)\} $ 
D)  $ \varnothing $; inconsistent system

Question 19

During the 1998-1999 Little League season, the Tigers played 47 games. They won 25 more games than they lost. How many games did they win that season?

Accepted Answer

A)  33 games 
B)  11 games 
C)  36 games 
D)  38 games 
A)  33 games 
B)  11 games 
C)  36 games 
D)  38 games

Question 20

$\frac{1}{3} x+\frac{1}{6} y-\frac{2}{3} z=-4$
$-\frac{3}{5} x-\frac{1}{3} y-\frac{1}{5} z=2$
$\frac{1}{2} x+\frac{3}{2} y+\frac{3}{4} z=13$

Accepted Answer

A)  $\left\{\left\{\frac{704}{203},-\frac{2078}{29},-\frac{704}{203}\right)\right\}$ 
B)  $\left\{\left\{-\frac{2078}{203},-\frac{300}{203}, \frac{704}{203}\right)\right\}$ 
C)  $\left\{\left\{\frac{2078}{29}, \frac{300}{29},-\frac{704}{29}\right)\right\}$ 
D)  $\left\{\left\{-\frac{2078}{203}, \frac{300}{29}, \frac{704}{203}\right)\right\}$ 
A)  $\left\{\left\{\frac{704}{203},-\frac{2078}{29},-\frac{704}{203}\right)\right\}$ 
B)  $\left\{\left\{-\frac{2078}{203},-\frac{300}{203}, \frac{704}{203}\right)\right\}$ 
C)  $\left\{\left\{\frac{2078}{29}, \frac{300}{29},-\frac{704}{29}\right)\right\}$ 
D)  $\left\{\left\{-\frac{2078}{203}, \frac{300}{29}, \frac{704}{203}\right)\right\}$

$7 \mathrm{x}-\mathrm{y}-4 \mathrm{z}=19$ $3 x-8 z=-4$ $7 \mathrm{y}+\mathrm{z}=9$

During the 1998-1999 Little League season, the Tigers played 51 games. They lost 15 more games than they won. How many games did they win that season?

In solving a system of three equations in three variables, the final step yields the following equation: $0=-1$ How many solutions does this system have? Explain geometrically.

$5 x+2 y+z=-11$ $2 x-3 y-z=17$ $7 \mathrm{x}+\mathrm{y}+2 \mathrm{z}=-4$

Tell how many solutions the system has. Do not actually solve. - $x-3 y=6$ $3 y+1=x$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $8 y-8=-x$ $2 x-5 y=-5$

$4 x-3 z=10$ $3 y+4 z=-9$ $\frac{1}{4} x+\frac{2}{3} y=-2$

The speed of a stream is $6 \mathrm{mph}$ . If a boat travels 54 miles downstream in the same time that it takes to travel 27 miles upstream, what is the speed of the boat in still water?

Candy and Delvis are riding bicycles in the same direction. Candy rides at a speed of 3 miles per hour, and Delvis rides at a speed of 9 miles per hour. If they started at the same place (and at the same time), then after 5 hours what is the distance between them?

During the 1998-1999 Junior Hockey League season, the Sharks played 44 games. Together, their wins and losses totaled 40 . They tied 8 fewer games than they lost. How many games did they lose that season?

Solving for which variable in which equation involves the least amount of work? $7 x=42$ $x-8 y=78$

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $x-4 y=-4$ $-4 x-3 y=-3$

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $3 x+4 y+z=18$ $2 \mathrm{x}-4 \mathrm{y}-\mathrm{z}=-3$ $4 \mathrm{x}+\mathrm{y}+5 \mathrm{z}=19$

Betsy doesn't trust banks, so her savings are hidden under her mattress. Alla has her savings in an investment at simple interest. During which years would Betsy's savings be more than Alla's?

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $x=22-4 y$ $5 x+3 y=8$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $y=1.5 x$ $0)5 \mathrm{x}+1.8 \mathrm{y}=6.4$

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - 2x+10y+10z=30 x+5y+5z=-10 x+y+z=-3

During the 1998-1999 Little League season, the Tigers played 47 games. They won 25 more games than they lost. How many games did they win that season?

$\frac{1}{3} x+\frac{1}{6} y-\frac{2}{3} z=-4$ $-\frac{3}{5} x-\frac{1}{3} y-\frac{1}{5} z=2$ $\frac{1}{2} x+\frac{3}{2} y+\frac{3}{4} z=13$

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

7x−y−4z=197 \mathrm{x}-\mathrm{y}-4 \mathrm{z}=197x−y−4z=19 3x−8z=−43 x-8 z=-43x−8z=−4 7y+z=97 \mathrm{y}+\mathrm{z}=97y+z=9

During the 1998-1999 Little League season, the Tigers played 51 games. They lost 15 more games than they won. How many games did they win that season?

In solving a system of three equations in three variables, the final step yields the following equation: 0=−10=-10=−1 How many solutions does this system have? Explain geometrically.

5x+2y+z=−115 x+2 y+z=-115x+2y+z=−11 2x−3y−z=172 x-3 y-z=172x−3y−z=17 7x+y+2z=−47 \mathrm{x}+\mathrm{y}+2 \mathrm{z}=-47x+y+2z=−4

Tell how many solutions the system has. Do not actually solve. - x−3y=6x-3 y=6x−3y=6 3y+1=x3 y+1=x3y+1=x

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

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - 8y−8=−x8 y-8=-x8y−8=−x 2x−5y=−52 x-5 y=-52x−5y=−5

4x−3z=104 x-3 z=104x−3z=10 3y+4z=−93 y+4 z=-93y+4z=−9 14x+23y=−2\frac{1}{4} x+\frac{2}{3} y=-241​x+32​y=−2

The speed of a stream is 6mph6 \mathrm{mph}6mph . If a boat travels 54 miles downstream in the same time that it takes to travel 27 miles upstream, what is the speed of the boat in still water?

Candy and Delvis are riding bicycles in the same direction. Candy rides at a speed of 3 miles per hour, and Delvis rides at a speed of 9 miles per hour. If they started at the same place (and at the same time), then after 5 hours what is the distance between them?

During the 1998-1999 Junior Hockey League season, the Sharks played 44 games. Together, their wins and losses totaled 40 . They tied 8 fewer games than they lost. How many games did they lose that season?

Solving for which variable in which equation involves the least amount of work? 7x=427 x=427x=42 x−8y=78x-8 y=78x−8y=78

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - x−4y=−4x-4 y=-4x−4y=−4 −4x−3y=−3-4 x-3 y=-3−4x−3y=−3

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - 3x+4y+z=183 x+4 y+z=183x+4y+z=18 2x−4y−z=−32 \mathrm{x}-4 \mathrm{y}-\mathrm{z}=-32x−4y−z=−3 4x+y+5z=194 \mathrm{x}+\mathrm{y}+5 \mathrm{z}=194x+y+5z=19

Betsy doesn't trust banks, so her savings are hidden under her mattress. Alla has her savings in an investment at simple interest. During which years would Betsy's savings be more than Alla's?

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - x=22−4yx=22-4 yx=22−4y 5x+3y=85 x+3 y=85x+3y=8

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - y=1.5xy=1.5 xy=1.5x 0)5x+1.8y=6.40)5 \mathrm{x}+1.8 \mathrm{y}=6.40)5x+1.8y=6.4

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - 2x+10y+10z=30 x+5y+5z=-10 x+y+z=-3

During the 1998-1999 Little League season, the Tigers played 47 games. They won 25 more games than they lost. How many games did they win that season?

13x+16y−23z=−4\frac{1}{3} x+\frac{1}{6} y-\frac{2}{3} z=-431​x+61​y−32​z=−4 −35x−13y−15z=2-\frac{3}{5} x-\frac{1}{3} y-\frac{1}{5} z=2−53​x−31​y−51​z=2 12x+32y+34z=13\frac{1}{2} x+\frac{3}{2} y+\frac{3}{4} z=1321​x+23​y+43​z=13

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

$7 \mathrm{x}-\mathrm{y}-4 \mathrm{z}=19$ $3 x-8 z=-4$ $7 \mathrm{y}+\mathrm{z}=9$

In solving a system of three equations in three variables, the final step yields the following equation: $0=-1$ How many solutions does this system have? Explain geometrically.

$5 x+2 y+z=-11$ $2 x-3 y-z=17$ $7 \mathrm{x}+\mathrm{y}+2 \mathrm{z}=-4$

Tell how many solutions the system has. Do not actually solve. - $x-3 y=6$ $3 y+1=x$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $8 y-8=-x$ $2 x-5 y=-5$

$4 x-3 z=10$ $3 y+4 z=-9$ $\frac{1}{4} x+\frac{2}{3} y=-2$

The speed of a stream is $6 \mathrm{mph}$ . If a boat travels 54 miles downstream in the same time that it takes to travel 27 miles upstream, what is the speed of the boat in still water?

Solving for which variable in which equation involves the least amount of work? $7 x=42$ $x-8 y=78$

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $x-4 y=-4$ $-4 x-3 y=-3$

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $3 x+4 y+z=18$ $2 \mathrm{x}-4 \mathrm{y}-\mathrm{z}=-3$ $4 \mathrm{x}+\mathrm{y}+5 \mathrm{z}=19$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $x=22-4 y$ $5 x+3 y=8$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $y=1.5 x$ $0)5 \mathrm{x}+1.8 \mathrm{y}=6.4$

$\frac{1}{3} x+\frac{1}{6} y-\frac{2}{3} z=-4$ $-\frac{3}{5} x-\frac{1}{3} y-\frac{1}{5} z=2$ $\frac{1}{2} x+\frac{3}{2} y+\frac{3}{4} z=13$