Question 1

Solve by addition or substitution.
-$x+y=15$
$\mathrm{x}-\mathrm{y}=-3$

Accepted Answer

A)  $(6,9)$ 
B)  $(-6,10)$ 
C)  $(5,10)$ 
D)  $\varnothing$ 
A)  $(6,9)$ 
B)  $(-6,10)$ 
C)  $(5,10)$ 
D)  $\varnothing$

Question 2

For the given system of equations, which method would be the most efficient method to use when solving the system of equations: substitution, addition, or either?
-$6 x-5 y=34$
$4 \mathrm{x}+3 \mathrm{y}=28$

Accepted Answer

A)  substitution 
B)  addition 
C)  either 
A)  substitution 
B)  addition 
C)  either

Question 3

The manager of a candy shop sells chocolate covered peanuts for $\$ 6$ per pound and chocolate covered cashews for $\$ 10$ per pound. The manager wishes to make a 40 - pound cashew- peanut mixture that will sell for $\$ 9$ per pound. How many pounds of each should be used?

Accepted Answer

A)  $35 \mathrm{lb}$ of peanuts 
B)  $20 \mathrm{lb}$ of peanuts $5 \mathrm{lb}$ of cashews $20 \mathrm{lb}$ of cashews 
C)  $10 \mathrm{lb}$ of peanuts
$30 \mathrm{lb}$ of cashews 
D)  $30 \mathrm{lb}$ of peanuts $10 \mathrm{lb}$ of cashews 
A)  $35 \mathrm{lb}$ of peanuts 
B)  $20 \mathrm{lb}$ of peanuts $5 \mathrm{lb}$ of cashews $20 \mathrm{lb}$ of cashews 
C)  $10 \mathrm{lb}$ of peanuts
$30 \mathrm{lb}$ of cashews 
D)  $30 \mathrm{lb}$ of peanuts $10 \mathrm{lb}$ of cashews

Question 4

Michael's bank contains only nickels, dimes, and quarters. There are 62 coins in all, valued at $\$$ 5.15. 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)  45 
B)  8 
C)  9 
D)  14 
A)  45 
B)  8 
C)  9 
D)  14

Question 5

Evaluate the determinant
-$\left|\begin{array}{lll}2 & 5 & 5 \ 3 & 5 & 2 \ 4 & 5 & 4\end{array}\right|$

Accepted Answer

A)  -105 
B)  -25 
C)  335 
D)  25 
A)  -105 
B)  -25 
C)  335 
D)  25

Question 6

In Marike's cash register there are only $\$ 5$ bills, $\$ 10$ bills, and $\$ 20$ bills. There are 176 bills in her cash register and their total value is $\$ 2095$. There are 35 more $\$ 10$ bills than $\$ 20$ bills. How many $\$ 20$ bills are in her cash register?

Accepted Answer

A)  56 
B)  87 
C)  48 
D)  52 
A)  56 
B)  87 
C)  48 
D)  52

Question 7

Graph the system of inequalities.
-$4 x+5 y \geq-9$
$y<-\frac{5}{2} x+7$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 8

Graph the system of inequalities.
-$x+2 y \geq 2$
$y \geq x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 9

Andy has 15 coins made up of quarters and half dollars, and their total value is $\$ 5.50$. How many quarters does he have?

Accepted Answer

A)  13 quarters 
B)  8 quarters 
C)  7 quarters 
D)  9 quarters 
A)  13 quarters 
B)  8 quarters 
C)  7 quarters 
D)  9 quarters

Question 10

Solve the system of equations using Cramer's rule.
-$0.7 x+0.09 y=212$
$\mathrm{x}-\mathrm{y}=-600$

Accepted Answer

A)  $(800,200)$ 
B)  $(200,800)$ 
C)  $(2,8)$ 
D)  $(200,-800)$ 
A)  $(800,200)$ 
B)  $(200,800)$ 
C)  $(2,8)$ 
D)  $(200,-800)$

Question 11

Graph the system of inequalities.
-$y \leq-2 x+4$
$\mathrm{x} \geq 1$

Accepted Answer

A) 
  
B) 
 . 
C) 
  
D) 
  
A) 
  
B) 
 . 
C) 
  
D)

Question 12

Sketch the feasible region, and use linear programming to find the maximum value of $\mathrm{z}$ on the feasible region.
-A college would like to offer a new course in ethnic studies and would like to offer some scholarship places to low-income students. The maximum number of students that can enroll for the course is 70 . The number of fee paying students must be at least 20 more than the number of scholarship students. Set up and graph a system of inequalities for the situation, letting $x$ represent the number of scholarship students and $y$ the number of fee- paying students.

Accepted Answer

The answer of Sketch the feasible region, and use linear...

Question 13

Solve the system of equations using matrices.
-$5 \mathrm{x}-\mathrm{y}-6 \mathrm{z}=-9$
$4 \mathrm{x}+9 \mathrm{z}=69$
$7 y+z=68$

Accepted Answer

A)  $(6,9,5)$ 
B)  $(6,5,9)$ 
C)  $(-6,5,9)$ 
D)  $(-6,9,12)$ 
A)  $(6,9,5)$ 
B)  $(6,5,9)$ 
C)  $(-6,5,9)$ 
D)  $(-6,9,12)$

Question 14

The manager of a candy shop sells chocolate covered peanuts for $\$ 7$ per pound and chooolate covered cashews for $\$ 14$ per pound. The manager wishes to make a 210- pound cashew- peanut mixture that will sell for $\$ 8$ per pound. How many pounds of each should be used?

Accepted Answer

A)  120 pounds of peanuts
90 pounds of cashews 
B)  105 pounds of peanuts 105 pounds of cashews 
C)  180 pounds of peanuts 30 pounds of cashews 
D)  30 pounds of peanuts 180 pounds of cashews 
A)  120 pounds of peanuts
90 pounds of cashews 
B)  105 pounds of peanuts 105 pounds of cashews 
C)  180 pounds of peanuts 30 pounds of cashews 
D)  30 pounds of peanuts 180 pounds of cashews

Question 15

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$.
-$x+y=4$
$4 \mathrm{x}+4 \mathrm{y}=16$

Accepted Answer

A)  $(x,-x+4)$ 
B)  $\varnothing$ 
C)  $(4,0)$ 
D)  $(0,0)$ 
A)  $(x,-x+4)$ 
B)  $\varnothing$ 
C)  $(4,0)$ 
D)  $(0,0)$

Question 16

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$.
-$9 x+y=23$
$9 x+y=77$

Accepted Answer

A)  $(18,5)$ 
B)  Dependent, $(\mathrm{x},-9 \mathrm{x}+23)$ 
C)  Inconsistent, $\varnothing$ 
D)  $(21,-166)$ 
A)  $(18,5)$ 
B)  Dependent, $(\mathrm{x},-9 \mathrm{x}+23)$ 
C)  Inconsistent, $\varnothing$ 
D)  $(21,-166)$

Question 17

$\begin{aligned} 7 x+7 y+z & =1 \ x+8 y+8 z & =8 \ 9 x+y+9 z & =9\end{aligned}$

Accepted Answer

A)  $(1,-1,1)$ 
B)  $(-1,1,1)$ 
C)  $(0,1,0)$ 
D)  $(0,0,1)$ 
A)  $(1,-1,1)$ 
B)  $(-1,1,1)$ 
C)  $(0,1,0)$ 
D)  $(0,0,1)$

Question 18

A woman made a deposit of $\$ 127$. If her deposit consisted of 43 bills, some of them one dollar bills and the rest being five- dollar bills, how many one- dollar bills did she deposit?

Accepted Answer

A)  21 one dollar bills 
B)  17 one- dollar bills 
C)  12 one dollar bills 
D)  22 one- dollar bills 
A)  21 one dollar bills 
B)  17 one- dollar bills 
C)  12 one dollar bills 
D)  22 one- dollar bills

Question 19

Michael's bank contains only nickels, dimes, and quarters. There are 46 coins in all, valued at $\$$ 4.20. The number of nickels is 10 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)  8 dimes 
B)  11 dimes 
C)  6 dimes 
D)  32 dimes 
A)  8 dimes 
B)  11 dimes 
C)  6 dimes 
D)  32 dimes

Question 20

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$.
-$3 x+y=13$
$9 x+3 y=39$

Accepted Answer

A)  Dependent, ( $\mathrm{x},-3 \mathrm{x}+13)$ 
B)  $(5,-2)$ 
C)  Inconsistent, $\varnothing$ 
D)  $(0,13)$ 
A)  Dependent, ( $\mathrm{x},-3 \mathrm{x}+13)$ 
B)  $(5,-2)$ 
C)  Inconsistent, $\varnothing$ 
D)  $(0,13)$

Solve by addition or substitution. - $x+y=15$ $\mathrm{x}-\mathrm{y}=-3$

For the given system of equations, which method would be the most efficient method to use when solving the system of equations: substitution, addition, or either? - $6 x-5 y=34$ $4 \mathrm{x}+3 \mathrm{y}=28$

The manager of a candy shop sells chocolate covered peanuts for $\$ 6$ per pound and chocolate covered cashews for $\$ 10$ per pound. The manager wishes to make a 40 - pound cashew- peanut mixture that will sell for $\$ 9$ per pound. How many pounds of each should be used?

Michael's bank contains only nickels, dimes, and quarters. There are 62 coins in all, valued at $\$$ 5.15. 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?

Evaluate the determinant - $\left|\begin{array}{lll}2 & 5 & 5 \\ 3 & 5 & 2 \\ 4 & 5 & 4\end{array}\right|$

In Marike's cash register there are only $\$ 5$ bills, $\$ 10$ bills, and $\$ 20$ bills. There are 176 bills in her cash register and their total value is $\$ 2095$ . There are 35 more $\$ 10$ bills than $\$ 20$ bills. How many $\$ 20$ bills are in her cash register?

Graph the system of inequalities. - $4 x+5 y \geq-9$ $y<-\frac{5}{2} x+7$ $Graph the system of inequalities. - 4 x+5 y \geq-9 y<-\frac{5}{2} x+7$

Graph the system of inequalities. - $x+2 y \geq 2$ $y \geq x$ $Graph the system of inequalities. - x+2 y \geq 2 y \geq x$

Andy has 15 coins made up of quarters and half dollars, and their total value is $\$ 5.50$ . How many quarters does he have?

Solve the system of equations using Cramer's rule. - $0.7 x+0.09 y=212$ $\mathrm{x}-\mathrm{y}=-600$

Graph the system of inequalities. - $y \leq-2 x+4$ $\mathrm{x} \geq 1$ $Graph the system of inequalities. - y \leq-2 x+4 \mathrm{x} \geq 1$

Solve the system of equations using matrices. - $5 \mathrm{x}-\mathrm{y}-6 \mathrm{z}=-9$ $4 \mathrm{x}+9 \mathrm{z}=69$ $7 y+z=68$

The manager of a candy shop sells chocolate covered peanuts for $\$ 7$ per pound and chooolate covered cashews for $\$ 14$ per pound. The manager wishes to make a 210- pound cashew- peanut mixture that will sell for $\$ 8$ per pound. How many pounds of each should be used?

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $x+y=4$ $4 \mathrm{x}+4 \mathrm{y}=16$

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $9 x+y=23$ $9 x+y=77$

7x+7y+z =1 x+8y+8z =8 9x+y+9z =9

A woman made a deposit of $\$ 127$ . If her deposit consisted of 43 bills, some of them one dollar bills and the rest being five- dollar bills, how many one- dollar bills did she deposit?

Michael's bank contains only nickels, dimes, and quarters. There are 46 coins in all, valued at $\$$ 4.20. The number of nickels is 10 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $3 x+y=13$ $9 x+3 y=39$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 4: Systems of Equations

Solve by addition or substitution. - x+y=15x+y=15x+y=15 x−y=−3\mathrm{x}-\mathrm{y}=-3x−y=−3

For the given system of equations, which method would be the most efficient method to use when solving the system of equations: substitution, addition, or either? - 6x−5y=346 x-5 y=346x−5y=34 4x+3y=284 \mathrm{x}+3 \mathrm{y}=284x+3y=28

The manager of a candy shop sells chocolate covered peanuts for $6\$ 6$6 per pound and chocolate covered cashews for $10\$ 10$10 per pound. The manager wishes to make a 40 - pound cashew- peanut mixture that will sell for $9\$ 9$9 per pound. How many pounds of each should be used?

Michael's bank contains only nickels, dimes, and quarters. There are 62 coins in all, valued at $\$$ 5.15. 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?

Evaluate the determinant - ∣255352454∣\left|\begin{array}{lll}2 & 5 & 5 \\ 3 & 5 & 2 \\ 4 & 5 & 4\end{array}\right|​234​555​524​​

In Marike's cash register there are only $5\$ 5$5 bills, $10\$ 10$10 bills, and $20\$ 20$20 bills. There are 176 bills in her cash register and their total value is $2095\$ 2095$2095 . There are 35 more $10\$ 10$10 bills than $20\$ 20$20 bills. How many $20\$ 20$20 bills are in her cash register?

Graph the system of inequalities. - 4x+5y≥−94 x+5 y \geq-94x+5y≥−9 y<−52x+7y<-\frac{5}{2} x+7y<−25​x+7

Graph the system of inequalities. - x+2y≥2x+2 y \geq 2x+2y≥2 y≥xy \geq xy≥x

Andy has 15 coins made up of quarters and half dollars, and their total value is $5.50\$ 5.50$5.50 . How many quarters does he have?

Solve the system of equations using Cramer's rule. - 0.7x+0.09y=2120.7 x+0.09 y=2120.7x+0.09y=212 x−y=−600\mathrm{x}-\mathrm{y}=-600x−y=−600

Graph the system of inequalities. - y≤−2x+4y \leq-2 x+4y≤−2x+4 x≥1\mathrm{x} \geq 1x≥1

Solve the system of equations using matrices. - 5x−y−6z=−95 \mathrm{x}-\mathrm{y}-6 \mathrm{z}=-95x−y−6z=−9 4x+9z=694 \mathrm{x}+9 \mathrm{z}=694x+9z=69 7y+z=687 y+z=687y+z=68

The manager of a candy shop sells chocolate covered peanuts for $7\$ 7$7 per pound and chooolate covered cashews for $14\$ 14$14 per pound. The manager wishes to make a 210- pound cashew- peanut mixture that will sell for $8\$ 8$8 per pound. How many pounds of each should be used?

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number xxx . - x+y=4x+y=4x+y=4 4x+4y=164 \mathrm{x}+4 \mathrm{y}=164x+4y=16

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number xxx . - 9x+y=239 x+y=239x+y=23 9x+y=779 x+y=779x+y=77

7x+7y+z =1 x+8y+8z =8 9x+y+9z =9

A woman made a deposit of $127\$ 127$127 . If her deposit consisted of 43 bills, some of them one dollar bills and the rest being five- dollar bills, how many one- dollar bills did she deposit?

Michael's bank contains only nickels, dimes, and quarters. There are 46 coins in all, valued at $\$$ 4.20. The number of nickels is 10 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number xxx . - 3x+y=133 x+y=133x+y=13 9x+3y=399 x+3 y=399x+3y=39

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Solve by addition or substitution. - $x+y=15$ $\mathrm{x}-\mathrm{y}=-3$

For the given system of equations, which method would be the most efficient method to use when solving the system of equations: substitution, addition, or either? - $6 x-5 y=34$ $4 \mathrm{x}+3 \mathrm{y}=28$

The manager of a candy shop sells chocolate covered peanuts for $\$ 6$ per pound and chocolate covered cashews for $\$ 10$ per pound. The manager wishes to make a 40 - pound cashew- peanut mixture that will sell for $\$ 9$ per pound. How many pounds of each should be used?

Evaluate the determinant - $\left|\begin{array}{lll}2 & 5 & 5 \\ 3 & 5 & 2 \\ 4 & 5 & 4\end{array}\right|$

In Marike's cash register there are only $\$ 5$ bills, $\$ 10$ bills, and $\$ 20$ bills. There are 176 bills in her cash register and their total value is $\$ 2095$ . There are 35 more $\$ 10$ bills than $\$ 20$ bills. How many $\$ 20$ bills are in her cash register?

Graph the system of inequalities. - $4 x+5 y \geq-9$ $y<-\frac{5}{2} x+7$ $Graph the system of inequalities. - 4 x+5 y \geq-9 y<-\frac{5}{2} x+7$

Graph the system of inequalities. - $x+2 y \geq 2$ $y \geq x$ $Graph the system of inequalities. - x+2 y \geq 2 y \geq x$

Andy has 15 coins made up of quarters and half dollars, and their total value is $\$ 5.50$ . How many quarters does he have?

Solve the system of equations using Cramer's rule. - $0.7 x+0.09 y=212$ $\mathrm{x}-\mathrm{y}=-600$

Graph the system of inequalities. - $y \leq-2 x+4$ $\mathrm{x} \geq 1$ $Graph the system of inequalities. - y \leq-2 x+4 \mathrm{x} \geq 1$

Solve the system of equations using matrices. - $5 \mathrm{x}-\mathrm{y}-6 \mathrm{z}=-9$ $4 \mathrm{x}+9 \mathrm{z}=69$ $7 y+z=68$

The manager of a candy shop sells chocolate covered peanuts for $\$ 7$ per pound and chooolate covered cashews for $\$ 14$ per pound. The manager wishes to make a 210- pound cashew- peanut mixture that will sell for $\$ 8$ per pound. How many pounds of each should be used?

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $x+y=4$ $4 \mathrm{x}+4 \mathrm{y}=16$

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $9 x+y=23$ $9 x+y=77$

A woman made a deposit of $\$ 127$ . If her deposit consisted of 43 bills, some of them one dollar bills and the rest being five- dollar bills, how many one- dollar bills did she deposit?

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $3 x+y=13$ $9 x+3 y=39$