Question 1

Solve the problem using the elimination method.
-The sum of two numbers is 100 . The second number is three times as large as the first number. What are the numbers?

Accepted Answer

A)  22 and 78 
B)  23 and 69 
C)  23 and 77 
D)  25 and 75 
A)  22 and 78 
B)  23 and 69 
C)  23 and 77 
D)  25 and 75

Question 2

Solve by the substitution method.
-$$\begin{array} { l } 
x + y = - 1 \
x + y = 4
\end{array}$$

Accepted Answer

A)  $( 0,3 )$ 
B)  No solution 
C)  $( 0,0 )$ 
D)  $( - 1,4 )$ 
A)  $( 0,3 )$ 
B)  No solution 
C)  $( 0,0 )$ 
D)  $( - 1,4 )$

Question 3

Solve the problem using the elimination method.
-There were 38,000 people at a ball game in Los Angeles. The day's receipts were $\$ 229,000$. How many people paid $\$ 11$ for reserved seats and how many paid $\$ 4$ for general admission?

Accepted Answer

A)  19,250 paid $\$ 11$ and 18,750 paid $\$ 4$ 
B)  27,000 paid $\$ 11$ and 11,000 paid $\$ 4$ 
C)  18,750 paid $\$ 11$ and 19,250 paid $\$ 4$ 
D)  11,000 paid $\$ 11$ and 27,000 paid $\$ 4$ 
A)  19,250 paid $\$ 11$ and 18,750 paid $\$ 4$ 
B)  27,000 paid $\$ 11$ and 11,000 paid $\$ 4$ 
C)  18,750 paid $\$ 11$ and 19,250 paid $\$ 4$ 
D)  11,000 paid $\$ 11$ and 27,000 paid $\$ 4$

Question 4

Solve the problem.
-How many liters of a $20 \%$ alcohol solution must be mixed with 90 liters of a $80 \%$ solution to get a $40 \%$ solution?

Accepted Answer

A)  $27 \mathrm {~L}$ 
B)  $18 \mathrm {~L}$ 
C)  $180 \mathrm {~L}$ 
D)  $270 \mathrm {~L}$ 
A)  $27 \mathrm {~L}$ 
B)  $18 \mathrm {~L}$ 
C)  $180 \mathrm {~L}$ 
D)  $270 \mathrm {~L}$

Question 5

Solve the problem using the elimination method.
-Two angles are supplementary, and one is $40 ^ { \circ }$ more than three times the other. Find the smaller angle.

Accepted Answer

A)  $145 ^ { \circ }$ 
B)  $105 ^ { \circ }$ 
C)  $75 ^ { \circ }$ 
D)  $35 ^ { \circ }$ 
A)  $145 ^ { \circ }$ 
B)  $105 ^ { \circ }$ 
C)  $75 ^ { \circ }$ 
D)  $35 ^ { \circ }$

Question 6

Solve the system of equations by the elimination method.
-$$\begin{array} { c } 
x + 5 y = 2 \
- 4 x + 6 y = - 8
\end{array}$$

Accepted Answer

A)  $( 2,0 )$ 
B)  no solution 
C)  $( 3,2 )$ 
D)  $( - 2 , - 1 )$ 
A)  $( 2,0 )$ 
B)  no solution 
C)  $( 3,2 )$ 
D)  $( - 2 , - 1 )$

Question 7

Solve.
-John and Tony start from GraysLake 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's speed $= \frac { 3 } { 5 } \mathrm {~m} / \mathrm { h }$ and John's $= \frac { 6 } { 5 } \mathrm {~m} / \mathrm { h }$. 
B)  Tony's speed $= \frac { 5 } { 3 } \mathrm {~m} / \mathrm { h }$ and John's $= \frac { 10 } { 3 } \mathrm {~m} / \mathrm { h }$. 
C)  Tony's speed $= 3 \mathrm {~m} / \mathrm { h }$ and John's $= 6 \mathrm {~m} / \mathrm { h }$. 
D)  Cannot be determined with information given 
A)  Tony's speed $= \frac { 3 } { 5 } \mathrm {~m} / \mathrm { h }$ and John's $= \frac { 6 } { 5 } \mathrm {~m} / \mathrm { h }$. 
B)  Tony's speed $= \frac { 5 } { 3 } \mathrm {~m} / \mathrm { h }$ and John's $= \frac { 10 } { 3 } \mathrm {~m} / \mathrm { h }$. 
C)  Tony's speed $= 3 \mathrm {~m} / \mathrm { h }$ and John's $= 6 \mathrm {~m} / \mathrm { h }$. 
D)  Cannot be determined with information given

Question 8

Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { l } 
x + y = - 11 \
x - y = - 5
\end{array}$$

Accepted Answer

A)  Inconsistent and independent 
B)  Inconsistent and dependent 
C)  Consistent and dependent 
D)  Consistent and independent 
A)  Inconsistent and independent 
B)  Inconsistent and dependent 
C)  Consistent and dependent 
D)  Consistent and independent

Question 9

Solve graphically.
-$\begin{array} { l } 
x = - 2 \
y = 1
\end{array}$

Accepted Answer

A)  Infinitely many solutions 
B)  No solution 
C)  $( - 2,1 )$ 
D)  $( 1 , - 2 )$ 
A)  Infinitely many solutions 
B)  No solution 
C)  $( - 2,1 )$ 
D)  $( 1 , - 2 )$

Question 10

Solve the problem.
-The sum of two numbers is 34 and their difference is 12. Find the numbers.

Accepted Answer

A) 23 and 11 
B) 25 and 37 
C) 9 and 25 
D) 11 and 23 
A) 23 and 11 
B) 25 and 37 
C) 9 and 25 
D) 11 and 23

Question 11

Classify the system as consistent or inconsistent, and dependent or independent.
-$\begin{array} { c } 
x + 5 y = 19 \
5 x - 6 y = 2
\end{array}$

Accepted Answer

A)  Inconsistent and independent 
B)  Consistent and independent 
C)  Consistent and dependent 
D)  Inconsistent and dependent 
A)  Inconsistent and independent 
B)  Consistent and independent 
C)  Consistent and dependent 
D)  Inconsistent and dependent

Question 12

Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { l } 
x - 8 = y \
y + 2 = x
\end{array}$$

Accepted Answer

A)  Inconsistent and independent 
B)  Consistent and independent 
C)  Consistent and dependent 
D)  Inconsistent and dependent 
A)  Inconsistent and independent 
B)  Consistent and independent 
C)  Consistent and dependent 
D)  Inconsistent and dependent

Question 13

Solve the problem.
-A merchant has coffee worth $\$ 20$ a pound that she wishes to mix with 90 pounds of coffee worth $\$ 90$ a pound to get a mixture that can be sold for $\$ 80$ a pound. How many pounds of the $\$ 20$ coffee should be used?

Accepted Answer

A)  $7.5 \mathrm { lb }$ 
B)  $52.5 \mathrm { lb }$ 
C)  $105 \mathrm { lb }$ 
D)  $15 \mathrm { lb }$ 
A)  $7.5 \mathrm { lb }$ 
B)  $52.5 \mathrm { lb }$ 
C)  $105 \mathrm { lb }$ 
D)  $15 \mathrm { lb }$

Question 14

Solve the system of equations by the elimination method.
-$$\begin{array} { l } 
9 x + 9 y = - 45 \
- 4 x - 6 y = 20
\end{array}$$

Accepted Answer

A)  $( - 5,1 )$ 
B)  no solution 
C)  $( - 5,0 )$ 
D)  $( - 6,1 )$ 
A)  $( - 5,1 )$ 
B)  no solution 
C)  $( - 5,0 )$ 
D)  $( - 6,1 )$

Question 15

Solve using the substitution method.
-$$\begin{array} { l } 
y = 2 x - 4 \
4 x + y = - 28
\end{array}$$

Accepted Answer

A)  $( - 5 , - 14 )$ 
B)  $( - 12 , - 4 )$ 
C)  $( - 12,20 )$ 
D)  $( - 4 , - 12 )$ 
A)  $( - 5 , - 14 )$ 
B)  $( - 12 , - 4 )$ 
C)  $( - 12,20 )$ 
D)  $( - 4 , - 12 )$

Question 16

Solve the problem.
-Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 28 pounds of feed worth $\$ 0.62$ per pound by mixing one kind worth $\$ 0.15$ per pound with another worth $\$ 0.97$ per pound. How many pounds of the cheaper kind should they use in the mix?

Accepted Answer

A)  21 pounds 
B)  14 pounds 
C)  12 pounds 
D)  16 pounds 
A)  21 pounds 
B)  14 pounds 
C)  12 pounds 
D)  16 pounds

Question 17

Solve the system of equations by the elimination method.
-$$\begin{array} { c } 
x - 3 y = - 5 \
4 x - 4 y = 12
\end{array}$$
$4 \mathrm { x } - 4 \mathrm { y } = 12$

Accepted Answer

A)  $( 7,4 )$ 
B)  $( 6,5 )$ 
C)  no solution 
D)  $( - 7,5 )$ 
A)  $( 7,4 )$ 
B)  $( 6,5 )$ 
C)  no solution 
D)  $( - 7,5 )$

Question 18

Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { c } 
x + 6 y = 17 \
2 x + 12 y = 34
\end{array}$$

Accepted Answer

A)  Inconsistent and dependent 
B)  Consistent and dependent 
C)  Inconsistent and independent 
D)  Consistent and independent 
A)  Inconsistent and dependent 
B)  Consistent and dependent 
C)  Inconsistent and independent 
D)  Consistent and independent

Question 19

Solve using the substitution method.
-$$\begin{array} { l } 
x + y = 16 \
y = 3 x + 4
\end{array}$$

Accepted Answer

A)  $( 4,12 )$ 
B)  $( 2,16 )$ 
C)  $( 3,13 )$ 
D)  $( 13,3 )$ 
A)  $( 4,12 )$ 
B)  $( 2,16 )$ 
C)  $( 3,13 )$ 
D)  $( 13,3 )$

Question 20

Solve using the substitution method.
-$$\begin{array} { l } 
x = 1 + - 2 y \
x + 2 y = 8
\end{array}$$

Accepted Answer

A)  Infinitely many solutions 
B)  $( - 7,15 )$ 
C)  $( - 7 , - 15 )$ 
D)  No solution 
A)  Infinitely many solutions 
B)  $( - 7,15 )$ 
C)  $( - 7 , - 15 )$ 
D)  No solution

Solve the problem using the elimination method. -The sum of two numbers is 100 . The second number is three times as large as the first number. What are the numbers?

Solve by the substitution method. - x+y=-1 x+y=4

Solve the problem using the elimination method. -There were 38,000 people at a ball game in Los Angeles. The day's receipts were $\$ 229,000$ . How many people paid $\$ 11$ for reserved seats and how many paid $\$ 4$ for general admission?

Solve the problem. -How many liters of a $20 \%$ alcohol solution must be mixed with 90 liters of a $80 \%$ solution to get a $40 \%$ solution?

Solve the problem using the elimination method. -Two angles are supplementary, and one is $40 ^ { \circ }$ more than three times the other. Find the smaller angle.

Solve the system of equations by the elimination method. - x+5y=2 -4x+6y=-8

Solve. -John and Tony start from GraysLake 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.

Classify the system as consistent or inconsistent, and dependent or independent. - x+y=-11 x-y=-5

Solve graphically. - x=-2 y=1 $Solve graphically. - \begin{array} { l } x = - 2 \\ y = 1 \end{array}$

Solve the problem. -The sum of two numbers is 34 and their difference is 12. Find the numbers.

Classify the system as consistent or inconsistent, and dependent or independent. - x+5y=19 5x-6y=2

Classify the system as consistent or inconsistent, and dependent or independent. - x-8=y y+2=x

Solve the problem. -A merchant has coffee worth $\$ 20$ a pound that she wishes to mix with 90 pounds of coffee worth $\$ 90$ a pound to get a mixture that can be sold for $\$ 80$ a pound. How many pounds of the $\$ 20$ coffee should be used?

Solve the system of equations by the elimination method. - 9x+9y=-45 -4x-6y=20

Solve using the substitution method. - y=2x-4 4x+y=-28

Solve the problem. -Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 28 pounds of feed worth $\$ 0.62$ per pound by mixing one kind worth $\$ 0.15$ per pound with another worth $\$ 0.97$ per pound. How many pounds of the cheaper kind should they use in the mix?

Solve the system of equations by the elimination method. - x-3y=-5 4x-4y=12 $4 \mathrm { x } - 4 \mathrm { y } = 12$

Classify the system as consistent or inconsistent, and dependent or independent. - x+6y=17 2x+12y=34

Solve using the substitution method. - x+y=16 y=3x+4

Solve using the substitution method. - x=1+-2y x+2y=8

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Finding Measures of Central Tendency for Prices and Heights

Filters

Exam 8: Systems of Equations