Deck 4: Systems of Linear Equations

Question 1

Decide whether the ordered pair is a solution of the given system

- $x+y=6$
$\mathrm{x}-\mathrm{y}=4 ;(5,1)$

Answer 1

False

Question 2

Decide whether the ordered pair is a solution of the given system

- $x+y=7$
$\mathrm{x}-\mathrm{y}=3 ;(-5,2)$

Answer 2

False

Question 3

Decide whether the ordered pair is a solution of the given system

- $4 x+y=25$
$2 \mathrm{x}+4 \mathrm{y}=16 ;(6,1)$

Answer 3

True

Question 4

Decide whether the ordered pair is a solution of the given system

- $4 x+y=-21$
$2 x+4 y=-14 ;(-5,1)$

Question 5

Solve the system by graphing.

- $\begin{array}{r}4 x+y=-17 \\ x+6 y=-10\end{array}$

A) $\{(-4,-5)\}$
B) $\{(4,-1)\}$
C) $\{(-4,-1)\}$
D) $\{(-5,3)\}$

Question 6

Solve the system by graphing.

- $-2 x+3 y=-1$
$3 x+2 y=21$

A) $\{(3,5)\}$
B) $\{(-2,27)\}$
C) $\{(5,3)\}$
D) $\varnothing$ ; inconsistent system

Question 7

Solve the system by graphing.

- $x-y=4$
$x+y=12$

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

Question 8

Solve the system by graphing.

- $y=13-6 x$
$x+6 y=-27$

A) $\{(3,-5)\}$
B) $\{(1,7)\}$
C) $\{(3,2)\}$
D) $\{(-3,-5)\}$

Question 9

Solve the system by graphing.

- $x=y-6$
$7 x=4 y$

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

Question 10

Solve the system by graphing.

- $y=x-6$
$y=-x+16$

A) $\{(10,22)\}$
B) $\{(11,5)\}$
C) $\{(22,10)\}$
D) $\{(5,11)\}$

Question 11

Solve the system by graphing.

- $4 x+4 y=28$
$4 x-2 y=16$

A) $\{(2,5)\}$
B) $\{(5,2)\}$
C) $\{(4,0)\}$
D) $\varnothing$ ; inconsistent system

Question 12

Solve the system by graphing.

- $x+y=-8$
$8 x-y=-64$

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

Question 13

Solve the system by graphing.

- $5 x+y=30$
$-x+y=-12$

A) $\{(7,-5)\}$
B) $\{(-7,5)\}$
C) $\{(-5,7)\}$
D) $\{(5,-7)\}$

Question 14

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

- $y=-\frac{5}{6} x$
$5 x-6 y=-4$

A) $\left\{\left(-\frac{2}{5},-\frac{1}{3}\right)\right\}$

B) $\left\{\left(\frac{2}{5}, \frac{1}{3}\right)\right\}$

C) $\left\{\left\{-\frac{2}{5}, \frac{1}{3}\right)\right\}$

D) $\varnothing$ ; inconsistent system

Question 15

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

- $x=22-4 y$
$5 x+3 y=8$

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

Question 16

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

- $x+y=-11$
$\mathrm{y}=-4 \mathrm{x}-5$

A) $\{(2,-13)\}$
B) $\{(1,-11)\}$
C) $\{(-13,2)\}$
D) $\{(3,-20)\}$

Question 17

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

- $8 y-8=-x$
$2 x-5 y=-5$

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

Question 18

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

- $5 x-2 y=-1$
$x+4 y=35$

A) $\{(3,8)\}$
B) $\{(2,8)\}$
C) $\{(2,9)\}$
D) $\{(3,9)\}$

Question 19

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

- $5 x+3 y=80$
$2 x+y=30$

A) $\{(0,10)\}$
B) $\{(0,0)\}$
C) $\{(10,10)\}$
D) $\{(10,0)\}$

Question 20

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

- $\frac{7}{3} x+\frac{5}{4} y=4$
$$\frac{5}{6} x-2 y=21$$

A) $\{(-6,-8)\}$
B) $\{(-6,8)\}$
C) $\{(6,8)\}$
D) $\{(6,-8)\}$

Question 21

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

- $x+y=-1$
$x+y=-6$

A) $\{(0,-7)\}$
B) $\varnothing$ ; inconsistent system
C) $\{(-1,-6)\}$
D) $\{(x, y) \mid x+y=-6\}$ ; dependent equations

Question 22

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

- $x+y=9$
$5 x+5 y=45$

A) $\{(0,0)\}$
B) $\{(x, y) \mid x+y=9\}$ ; dependent equations
C) $\{(8,1)\}$
D) $\varnothing$ ; inconsistent system

Question 23

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

- $y=1.5 x$
$0)5 \mathrm{x}+1.8 \mathrm{y}=6.4$

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

Question 24

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

- $-x+6 y=9$
$8 x-6 y=54$

A) $\{(10,2)\}$
B) $\{(9,3)\}$
C) $\{(-3,9)\}$
D) $\varnothing$ ; inconsistent system

Question 25

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

- $x+4 y=13$
$2 x+3 y=6$

A) $\{(-3,4)\}$
B) $\{(3,5)\}$
C) $\{(-4,5)\}$
D) $\varnothing$ ; inconsistent system

Question 26

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

- $x-4 y=-4$
$-4 x-3 y=-3$

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

Question 27

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

- $x-3 y=-3$
$7 \mathrm{x}-2 \mathrm{y}=-21$

A) $\{(-2,-1)\}$
B) $\{(-2,-3)\}$
C) $\{(-3,0)\}$
D) $\varnothing$ ; inconsistent system

Question 28

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

- $6 x+9 y=69$
$-2 x-3 y=-23$

A) $\{(-3,10)\}$
B) $\{(-2,9)\}$
C) $\{(-2,10)\}$
D) $\varnothing$ ; inconsistent system

Question 29

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

- $8 x+6 y=24$
$-3 x+2 y=8$

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

Question 30

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

- $-7 x+9 y=-42$
$-5 x+2 y=-30$

A) $\{(6,1)\}$
B) $\{(5,1)\}$
C) $\{(6,0)\}$
D) $\varnothing$ ; inconsistent system

Question 31

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

- $5 x-2 y=3$
$-20 x+8 y=-12$

A) $\{(-3,-9)\}$
B) $\{(1,1)\}$
C) $\{(x, y) \mid 5 x-2 y=3\}$ ; dependent equations
D) $\varnothing$ ; inconsistent system

Question 32

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

- $2 x-3 y=-2$
$6 x-9 y=6$

A) $\{(-1,0)\}$
B) $\{(5,-4)\}$
C) $\{(x, y) \mid 2 x-3 y=-2\}$ ; dependent equations
D) $\varnothing$ ; inconsistent system

Question 33

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

- $\frac{1}{5} x-\frac{1}{4} y=1$

$\frac{2}{5} x+\frac{1}{2} y=2$

A) $\{(-5,-2)\}$

B) $\{(5,0)\}$

C) $\{(-5,0)\}$

D) $\varnothing$ ; inconsistent system

Question 34

Tell how many solutions the system has. Do not actually solve.

- $2 x+5 y=-1$
$4 x+10 y=-2$

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

Question 35

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) Infinitely many
B) No solution
C) One solution

Question 36

Tell how many solutions the system has. Do not actually solve.

- $3 x-y=7$
$x+6 y=34$

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

Question 37

Tell how many solutions the system has. Do not actually solve.

- $x-3=y$
$y+7=x$

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

Question 38

Tell how many solutions the system has. Do not actually solve.

- $2 x-y=5$
$-4 x+2 y=-18$

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

Question 39

Tell how many solutions the system has. Do not actually solve.

- $x-2 y=5$
$2 x-4 y=18$

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

Question 40

Tell how many solutions the system has. Do not actually solve.

- $3 x=y+3$
$6 x-2 y=3$

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

Question 41

Tell how many solutions the system has. Do not actually solve.

- $x+2 y=0$
$y=-\frac{1}{2} x$

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

Question 42

Tell how many solutions the system has. Do not actually solve.

- $2 x+3 y=6$
$4 x+6 y=12$

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

Question 43

Tell how many solutions the system has. Do not actually solve.

- $x-3 y=6$
$3 y+1=x$

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

Question 44

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 coordinates of the point of intersection of the graphs.

A) $(7,7)$
B) $(7,2)$
C) $(3,9)$
D) $(2,7)$

Question 45

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 $\mathrm{y} 1$ .

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 46

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 $\mathrm{y}_{2}$ .

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

Question 47

The table shown was generated by a graphing calculator. The functions defined by $y_{1}$ and y2 are linear. Based on the table, solve the system of equations formed by $\mathrm{y}_{1}$ and $\mathrm{y}_{2}$ .

A) $\{(3,9)\}$
B) $\{(7,2)\}$
C) $\{(2,7)\}$
D) $\{(9,3)\}$

Question 48

The solution set of the system $y_{1}=2 x+3$ and $y_{2}=-x+9$ is $\{(2,7)\}$ . Using slopes and $y$ -intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

A) Neither is correct.
B) Right
C) Left
D) Both could be correct.

Question 49

The solution set of the system $y_{1}=-x+5$ and $y_{2}=-2 x+7$ is $\{(2,3)\}$ . Using slopes and $y$ -intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

A) Left
B) Right
C) Both could be correct.
D) Neither is correct.

Question 50

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?

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

Question 51

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?

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

Question 52

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?

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

Question 53

Emilia doesn't trust banks, so her savings are hidden under her mattress. Deepak has his savings in an investment at simple interest. During which year did they have the same amount?

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

Question 54

The graphs below represent the supply and demand for a product at various prices per unit. At approximately what price does supply equal demand?

A) $\$ 400$
B) $\$ 650$
C) $\$ 177$
D) $\$ 900$

Question 55

The graphs below represent the supply and demand for a product at various prices per unit. Approximately how many units should be produced so that supply equals demand?

A) 2250 units
B) 42,900 units
C) 2255 units
D) 42.9 units

Question 56

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

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

Question 57

A company manufactures three products. The graph shows the production from 1986 to 1996 . What was the approximate level of production when the production of A equaled the production of $\mathrm{B}$ ?

A) 800,000
B) 700,000
C) 500,000
D) 400,000

Question 58

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. After how many years does the variable plan pay less per month than the fixed plan?

A) Up to 8 years
B) 8 years
C) 9 years
D) The variable plan always pays less.

Question 59

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?

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

Question 60

Solve the system of equations.

- $\frac{6}{x}-\frac{3}{y}=-13$
$\frac{3}{x}+\frac{1}{y}=6$

A) $\left\{\left\{\left(\frac{1}{5}, 3\right)\right\}\right.$

B) $\left\{\left\{\left(\frac{1}{3}, 5\right)\right\}\right.$

C) $\left\{\left\{3, \frac{1}{5}\right)\right\}$

D) $\varnothing$

Question 61

Solve the system of equations.

- $\frac{6}{y}+\frac{2}{x}=\frac{23}{20}$
$\frac{4}{y}-\frac{2}{x}=\frac{1}{10}$

A) $\{(5,8\})$

B) $\varnothing$

C) $\{(-5,8\})$

D) $\left\{\left\{\left(\frac{1}{5}, \frac{1}{8}\right)\right\}\right.$

Question 62

Solve the system of equations.

- $\frac{4}{y}+\frac{2}{x}=-\frac{1}{2}$
$\frac{5}{y}+\frac{4}{x}=-\frac{1}{4}$

A) $\left\{\left\{\left(\frac{1}{4},-\frac{1}{4}\right)\right\}\right.$

B) $\varnothing$

C) $\{(4,4\})$

D) $\{(4,-4\})$

Question 63

Solve by any method. Assume $a$ and $b$ represent nonzero constants.

- $4 a x+3 y=1$
$y=2 a x$

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 64

Solve by any method. Assume $a$ and $b$ represent nonzero constants.

- $7 \mathrm{ax}-2 \mathrm{y}=2$
$\mathrm{y}=5 \mathrm{ax}$

A) $\left\{\left\{-\frac{2}{3},-\frac{10}{3}\right)\right\}$

B) $\left\{\left\{-\frac{10}{3},-\frac{2}{3 a}\right)\right\}$

C) $\left\{\left\{-\frac{2 a}{3},-\frac{10}{3}\right)\right\}$

D) $\left\{\left\{-\frac{2}{3 a},-\frac{10}{3}\right)\right\}$

Question 65

Solve by any method. Assume $a$ and $b$ represent nonzero constants.

- $\mathrm{ax}+\mathrm{by}=2$
$2 \mathrm{ax}+4 \mathrm{by}=1$

A) $\left\{\left\{\frac{7 b}{2},-\frac{3 a}{2}\right)\right\}$

B) $\left\{\left\{-\frac{3}{2 b}, \frac{7}{2 a}\right)\right\}$

C) $\left\{\left\{\left(\frac{7 a}{2},-\frac{3}{2 b}\right)\right\}\right.$

D) $\left\{\left\{\left(\frac{7}{2 a},-\frac{3}{2 b}\right)\right\}\right.$

Question 66

Solve by any method. Assume $a$ and $b$ represent nonzero constants.

- $a x+b y=1$
Ax - by $=14$

A) $\left\{\left(\frac{15}{2 a},-\frac{13}{2 b}\right)\right\}$

B) $\left\{\left\{\frac{13}{a},-\frac{15}{2 b}\right)\right\}$

C) $\left\{\left(\frac{15}{2 a}, \frac{13}{2 b}\right)\right\}$

D) $\left\{\left(-\frac{15}{2 a},-\frac{13}{2 b}\right)\right\}$

Question 67

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response
-Give the definition or an example of the word or phrase.
Dependent system

Question 68

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?

Question 69

Graphs of two linear functions $f$ and $g$ that are neither parallel nor coincident intersect in how many points?

A) None
B) Two
C) One
D) Infinitely many points

Question 70

Write the word or phrase that best completes each statement or answers the question

-What is indicated by the occurrence of a true statement such as " $0=0$ " when you solve a system of two linear equation (in two variables) using elimination?

Question 71

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

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

Question 72

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

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

Question 73

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

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

Question 74

$7 x+7 y+z=1$
$x+8 y+8 z=8$
$9 \mathrm{x}+\mathrm{y}+9 \mathrm{z}=9$

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

Question 75

$x+y+z=5$
$x-y+5 z=-3$
$5 x+y+z=21$

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

Question 76

$3 x+3 y+z=1$
$4 x-5 y-z=-28$
$3 \mathrm{x}+\mathrm{y}+3 \mathrm{z}=-3$

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

Question 77

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

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) $\left\{\left\{-\frac{2078}{203}, \frac{300}{29}, \frac{704}{203}\right)\right\}$

Question 78

$2.4 x+3.5 y-1.7 z=24.72$
$0.3 x-1.7 y+5.1 z=-26.60$
$5.1 x-2.7 y-8.5 z=35.06$

A) $\{(2.0,3.7,-4.1)\}$
B) $\{(4,3.7,-12.3)\}$
C) $\{(2.0,-3.7,-4.1)\}$
D) $\{(2.0,3.7,4.1)\}$

Question 79

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

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

Question 80

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

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