Question 1

Solve the system by any method, if possible. If the system is inconsistent, or if the equations are dependent, so indicate. $\left\{ \begin{array} { c } 
0.04 x - 0.02 y = 0.08 \
2 x - 4 = y
\end{array} \right.$

Accepted Answer

The answer of Solve the system by any method, if...

Question 2

Solve the system by substitution, if possible. $$\left\{ \begin{array} { c } 
x + 2 y = 7 \
3 x - 2 y = - 14
\end{array} \right.$$

Accepted Answer

A)  $( - 3,5 )$ 
B)  $( 5,3 )$ 
C)  $( 3,5 )$ 
D) infinitely many solutions, dependent equations 
E) no solution, inconsistent system

Question 3

Graph the solution of the system: $$\left\{ \begin{array} { c } 
x - 2 y < 4 \
y < \frac { x } { 2 } - 5
\end{array} \right.$$

Accepted Answer

A)   
B)   
C)   
D)

Question 4

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $$\left\{ \begin{array} { c } 
7 a + 9 b = 69 \
a = 21 - 5 b
\end{array} \right.$$

Accepted Answer

A)  $( 6,3 )$ 
B)  $( 6 , - 3 )$ 
C)  $( - 6,3 )$ 
D) The equations are dependent. 
E) The system is inconsistent.

Question 5

A distributor wholesales desk chairs for $200 and side chairs for $100. Best Furniture wants to order no more than $1,200 worth of chairs and wants to order more side chairs than desk chairs. Find a system of inequalities whose graph will show the possible combination of desk chairs ( x )and side chairs ( y )that can be ordered, graph the system of inequalities, and determine whether the ordered pairs satisfy the inequality.

Accepted Answer

A)  $\left\{ \begin{array} { c } 
200 x + 100 y  x
\end{array} \right.$  $( 0,10 ) , ( 0,11 )$ 
C)  $\left\{ \begin{array} { c } 
200 x + 100 y \leq 1,200 \
y  x
\end{array} \right.$  $( 0,3 ) , ( 11,0 )$ 
E)  $\left\{ \begin{array} { c } 
200 x + 100 y \geq 1,200 \
y > x
\end{array} \right.$  $( 4,3 ) , ( 0,10 )$

Question 6

Use two equations in two variables to solve the following problem. In a year the number of people dying from cancer was 6 times the number who died from accidents. If the number of deaths from these two causes totaled 280,000, how many people died from each cause?

Accepted Answer

A) 220,000 died from cancer, 40,000 died from accidents 
B) 250,000 died from cancer, 30,000 died from accidents 
C) 220,000 died from cancer, 60,000 died from accidents 
D) 240,000 died from cancer, 40,000 died from accidents 
E) 250,000 died from cancer, 60,000 died from accidents

Question 7

An airplane can fly with the wind a distance of 920 miles in 4 hours. However, the return trip against the wind takes 5 hours. Find the speed of the plane in still air and the speed of the wind.

Accepted Answer

A) 211 mph, 19 mph 
B) 203 mph, 27 mph 
C) 207 mph, 22 mph 
D) 207 mph, 23 mph 
E) 230 mph, 23 mph

Question 8

Solve the system by any method, if possible. $$\left\{ \begin{array} { c } 
0.18 x - 0.09 y = 0.36 \
2 x - 4 = y
\end{array} \right.$$

Accepted Answer

A)  $\left( \frac { 3 } { 2 } , 0.36 \right)$ 
B)  $\left( 0.18 , \frac { 3 } { 2 } \right)$ 
C)  $\left( 0.36 , \frac { 3 } { 2 } \right)$ 
D) infinitely many solutions, dependent equations 
E) no solution, inconsistent system

Question 9

A box contains $7.85 in nickels, dimes, and quarters. There are 48 coins in all, and the sum of the numbers of nickels and dimes is two less than the number of quarters. How many coins of each kind are there?

Accepted Answer

A) 17 nickels, 8 dimes, and 23 quarters 
B) 16 nickels, 7 dimes, and 25 quarters 
C) 16 nickels, 12 dimes, and 28 quarters 
D) 14 nickels, 9 dimes, and 25 quarters 
E) 17 nickels, 11 dimes, and 20 quarters

Question 10

Solve the system. $$\left\{ \begin{array} { c } 
3 x - 6 y = 18 \
x = 2 y + 3
\end{array} \right.$$

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Without graphing, determine the number of solutions of: $$\left\{ \begin{array} { l } 
6 x - y = - 3 \
18 x + 9 = 3 y
\end{array} \right.$$

Accepted Answer

A) No solutions 
B) One solution 
C) Two solutions 
D) Infinitely many solutions

Question 12

Part of $10,000 is invested at 9%, another part at 10%, and the remainder at 12% yearly interest. The total yearly income from the three investments is $1,075. The sum of the amounts invested at 9% and 10% equals the amount invested at 12%. How much is invested at each rate?

Accepted Answer

A) $2,500 at 9%, $2,500 at 10%, and $5,000 at 12% 
B) $3,500 at 9%, $3,500 at 10%, and $4,000 at 12% 
C) $1,500 at 9%, $3,500 at 10%, and $5,000 at 12% 
D) $3,500 at 9%, $2,500 at 10%, and $4,000 at 12% 
E) $1,500 at 9%, $1,500 at 10%, and $6,000 at 12%

Question 13

A tree casts a shadow of 26 feet at the same time as a 6-foot man casts a shadow of 4 feet. Find the height of the tree.

Accepted Answer

A) 41 feet 
B) 35 feet 
C) 39 feet 
D) 31 feet 
E) 52 feet

Question 14

One day last summer, Jim went kayaking on the Little Susitna River in Alaska. Paddling upstream against the current, he traveled 45 miles in 5 hours. Then he turned around and paddled twice as fast downstream and, with the help of the current, traveled 27 miles in 1 hour. Find the rate of the current.

Accepted Answer

A) 3 mph 
B) 27 mph 
C) 12 mph 
D) 15 mph 
E) 9 mph

Question 15

Without graphing, determine the number of solutions of: $$\left\{ \begin{array} { l } 
4 y = - 2 x + 4 \
4 x + 8 y = 5
\end{array} \right.$$

Accepted Answer

A) No solutions 
B) One solution 
C) Two solutions 
D) Infinitely many solutions

Question 16

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $$\left( \begin{array} { c } 
3 x - 8 y = 3 \
6 x - 16 y = - 2
\end{array} \right)$$

Accepted Answer

A) (-1, 1) 
B) (2, 3) 
C) (2, 1) 
D) dependent 
E) inconsistent

Question 17

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $$\left\{ \begin{array} { l } 
5 ( x - 1 ) + 23 = 43 - 3 y \
9 ( x + 1 ) + 35 = 82 - 4 y
\end{array} \right.$$

Accepted Answer

A)  $( 2,5 )$ 
B)  $( 5,2 )$ 
C)  $( - 2 , - 5 )$ 
D) The equations are dependent. 
E) The system is inconsistent.

Question 18

A boat traveled 48 miles downstream in 4 hours and made the return trip in 6 hours. Find the rate of the current.

Accepted Answer

A) 10 mph 
B) 2 mph 
C) 3 mph 
D) 4 mph

Question 19

Use two equations in two variables to solve the following problem. A rancher raises five times as many cows as horses. If he has 144 animals (cows and horses only), how many cows does he have?

Accepted Answer

A) 120 cows 
B) 100 cows 
C) 160 cows 
D) 110 cows 
E) 90 cows

Question 20

Use the substitution method to solve the following system: $$\left\{ \begin{array} { c } 
0.07 x + 0.04 y = 0.3 \
x = \frac { y } { 2 }
\end{array} \right.$$

Accepted Answer

A) (-1, -2) 
B) (0, 0) 
C) (2, 4) 
D) The equations are dependent. 
E) The system is inconsistent.

Exam 4: Solving Systems of Equations and Inequalities

Solve the system by any method, if possible. If the system is inconsistent, or if the equations are dependent, so indicate. $\left\{ \begin{array} { c } 0.04 x - 0.02 y = 0.08 \\2 x - 4 = y\end{array} \right.$

Solve the system by substitution, if possible. $\left\{ \begin{array} { c } x + 2 y = 7 \\3 x - 2 y = - 14\end{array} \right.$

Graph the solution of the system: $\left\{ \begin{array} { c } x - 2 y < 4 \\y < \frac { x } { 2 } - 5\end{array} \right.$

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { c } 7 a + 9 b = 69 \\a = 21 - 5 b\end{array} \right.$

Use two equations in two variables to solve the following problem. In a year the number of people dying from cancer was 6 times the number who died from accidents. If the number of deaths from these two causes totaled 280,000, how many people died from each cause?

An airplane can fly with the wind a distance of 920 miles in 4 hours. However, the return trip against the wind takes 5 hours. Find the speed of the plane in still air and the speed of the wind.

Solve the system by any method, if possible. $\left\{ \begin{array} { c } 0.18 x - 0.09 y = 0.36 \\2 x - 4 = y\end{array} \right.$

A box contains $7.85 in nickels, dimes, and quarters. There are 48 coins in all, and the sum of the numbers of nickels and dimes is two less than the number of quarters. How many coins of each kind are there?

Solve the system. $\left\{ \begin{array} { c } 3 x - 6 y = 18 \\x = 2 y + 3\end{array} \right.$

Without graphing, determine the number of solutions of: $\left\{ \begin{array} { l } 6 x - y = - 3 \\18 x + 9 = 3 y\end{array} \right.$

Part of $10,000 is invested at 9%, another part at 10%, and the remainder at 12% yearly interest. The total yearly income from the three investments is $1,075. The sum of the amounts invested at 9% and 10% equals the amount invested at 12%. How much is invested at each rate?

A tree casts a shadow of 26 feet at the same time as a 6-foot man casts a shadow of 4 feet. Find the height of the tree.

Without graphing, determine the number of solutions of: $\left\{ \begin{array} { l } 4 y = - 2 x + 4 \\4 x + 8 y = 5\end{array} \right.$

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { c } 3 x - 8 y = 3 \\6 x - 16 y = - 2\end{array} \right)$

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { l } 5 ( x - 1 ) + 23 = 43 - 3 y \\9 ( x + 1 ) + 35 = 82 - 4 y\end{array} \right.$

A boat traveled 48 miles downstream in 4 hours and made the return trip in 6 hours. Find the rate of the current.

Use two equations in two variables to solve the following problem. A rancher raises five times as many cows as horses. If he has 144 animals (cows and horses only) , how many cows does he have?

Use the substitution method to solve the following system: $\left\{ \begin{array} { c } 0.07 x + 0.04 y = 0.3 \\x = \frac { y } { 2 }\end{array} \right.$

Exam 4: Solving Systems of Equations and Inequalities

Solve the system by any method, if possible. If the system is inconsistent, or if the equations are dependent, so indicate. {0.04x−0.02y=0.082x−4=y\left\{ \begin{array} { c } 0.04 x - 0.02 y = 0.08 \\2 x - 4 = y\end{array} \right.{0.04x−0.02y=0.082x−4=y​

Solve the system by substitution, if possible. {x+2y=73x−2y=−14\left\{ \begin{array} { c } x + 2 y = 7 \\3 x - 2 y = - 14\end{array} \right.{x+2y=73x−2y=−14​

Graph the solution of the system: {x−2y<4y<x2−5\left\{ \begin{array} { c } x - 2 y < 4 \\y < \frac { x } { 2 } - 5\end{array} \right.{x−2y<4y<2x​−5​

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. {7a+9b=69a=21−5b\left\{ \begin{array} { c } 7 a + 9 b = 69 \\a = 21 - 5 b\end{array} \right.{7a+9b=69a=21−5b​

Use two equations in two variables to solve the following problem. In a year the number of people dying from cancer was 6 times the number who died from accidents. If the number of deaths from these two causes totaled 280,000, how many people died from each cause?

An airplane can fly with the wind a distance of 920 miles in 4 hours. However, the return trip against the wind takes 5 hours. Find the speed of the plane in still air and the speed of the wind.

Solve the system by any method, if possible. {0.18x−0.09y=0.362x−4=y\left\{ \begin{array} { c } 0.18 x - 0.09 y = 0.36 \\2 x - 4 = y\end{array} \right.{0.18x−0.09y=0.362x−4=y​

A box contains $7.85 in nickels, dimes, and quarters. There are 48 coins in all, and the sum of the numbers of nickels and dimes is two less than the number of quarters. How many coins of each kind are there?

Solve the system. {3x−6y=18x=2y+3\left\{ \begin{array} { c } 3 x - 6 y = 18 \\x = 2 y + 3\end{array} \right.{3x−6y=18x=2y+3​

Without graphing, determine the number of solutions of: {6x−y=−318x+9=3y\left\{ \begin{array} { l } 6 x - y = - 3 \\18 x + 9 = 3 y\end{array} \right.{6x−y=−318x+9=3y​

Part of $10,000 is invested at 9%, another part at 10%, and the remainder at 12% yearly interest. The total yearly income from the three investments is $1,075. The sum of the amounts invested at 9% and 10% equals the amount invested at 12%. How much is invested at each rate?

A tree casts a shadow of 26 feet at the same time as a 6-foot man casts a shadow of 4 feet. Find the height of the tree.

Without graphing, determine the number of solutions of: {4y=−2x+44x+8y=5\left\{ \begin{array} { l } 4 y = - 2 x + 4 \\4 x + 8 y = 5\end{array} \right.{4y=−2x+44x+8y=5​

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. (3x−8y=36x−16y=−2) \left( \begin{array} { c } 3 x - 8 y = 3 \\6 x - 16 y = - 2\end{array} \right) (3x−8y=36x−16y=−2​)

A boat traveled 48 miles downstream in 4 hours and made the return trip in 6 hours. Find the rate of the current.

Use two equations in two variables to solve the following problem. A rancher raises five times as many cows as horses. If he has 144 animals (cows and horses only) , how many cows does he have?

Use the substitution method to solve the following system: {0.07x+0.04y=0.3x=y2\left\{ \begin{array} { c } 0.07 x + 0.04 y = 0.3 \\x = \frac { y } { 2 }\end{array} \right.{0.07x+0.04y=0.3x=2y​​

Solve the system by any method, if possible. If the system is inconsistent, or if the equations are dependent, so indicate. $\left\{ \begin{array} { c } 0.04 x - 0.02 y = 0.08 \\2 x - 4 = y\end{array} \right.$

Solve the system by substitution, if possible. $\left\{ \begin{array} { c } x + 2 y = 7 \\3 x - 2 y = - 14\end{array} \right.$

Graph the solution of the system: $\left\{ \begin{array} { c } x - 2 y < 4 \\y < \frac { x } { 2 } - 5\end{array} \right.$

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. $\left\{ \begin{array} { c } 7 a + 9 b = 69 \\a = 21 - 5 b\end{array} \right.$

Solve the system by any method, if possible. $\left\{ \begin{array} { c } 0.18 x - 0.09 y = 0.36 \\2 x - 4 = y\end{array} \right.$

Solve the system. $\left\{ \begin{array} { c } 3 x - 6 y = 18 \\x = 2 y + 3\end{array} \right.$

Without graphing, determine the number of solutions of: $\left\{ \begin{array} { l } 6 x - y = - 3 \\18 x + 9 = 3 y\end{array} \right.$

Without graphing, determine the number of solutions of: $\left\{ \begin{array} { l } 4 y = - 2 x + 4 \\4 x + 8 y = 5\end{array} \right.$

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { c } 3 x - 8 y = 3 \\6 x - 16 y = - 2\end{array} \right)$

Use the substitution method to solve the following system: $\left\{ \begin{array} { c } 0.07 x + 0.04 y = 0.3 \\x = \frac { y } { 2 }\end{array} \right.$