Question 1

​Solve the system of linear equations by the method of elimination,find (x,y). ​​ $$\left\{ \begin{array} { l } 
- 0.06 x + 0.01 y = 0.03 \
- 0.09 x - 0.04 y = 0.09
\end{array} \right.$$ ​

Accepted Answer

A) ​ $\left( - \frac { 11 } { 7 } , - \frac { 11 } { 9 } \right)$ 
B)  $\left( - \frac { 14 } { 11 } , - \frac { 9 } { 11 } \right)$ 
C) ​ $\left( - \frac { 7 } { 11 } , - \frac { 27 } { 11 } \right)$ 
D) No solution 
E) ​ $\left( - \frac { 7 } { 11 } , - \frac { 9 } { 11 } \right)$

Question 2

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ $$\left\{ \begin{array} { l } 
3 x + 11 y = 12 \
- 2 x - 5 y = 6
\end{array} \right.$$ ​

Accepted Answer

A) ​(18,6) 
B) (-18,-6) ​ 
C) (-18,18) 
D) (-18,6) 
E) ​(18,-6) ​

Question 3

Thirty​ liters of a 40% acid solution is obtained by mixing a 28% solution with a 43% solution.How much of each solution is required to obtain the specified concentration of the final mixture? Use this system of linear equations there x and y represents the amounts of the 28% solution and 43% solution. ​​ $$\left\{ \begin{array} { l } 
x + y = 30 \
0.28 x + 0.43 y = 12
\end{array} \right.$$ ​

Accepted Answer

A) ​28% solution: 6 L;43% solution: 24 L 
B) 43% solution: 6 L;28% solution: 24 L​ 
C) ​28% solution: 40 L;43% solution: 24 L 
D) ​43% solution: 40 L;28% solution: 24 L 
E) ​43% solution: 7 L;28% solution: 24 L

Question 4

​Solve the system of linear equations using any method,find (x,y). ​​ $$\left\{ \begin{array} { r } 
9 x - 2 y = 1 \
- 3 x + 2 y = 7
\end{array} \right.$$ ​

Accepted Answer

A) ​ $\left( \frac { 3 } { 4 } , \frac { 2 } { 11 } \right)$ 
B) ​ $\left( \frac { 8 } { 3 } , \frac { 11 } { 2 } \right)$ 
C) ​No solution 
D) ​ $\left( \frac { 4 } { 3 } , \frac { 11 } { 2 } \right)$ 
E) ​ $\left( \frac { 1 } { 3 } , \frac { 5 } { 2 } \right)$

Question 5

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ $$\left\{ \begin{array} { c } 
5 x + 3 y = 6 \
3 x - y = 5
\end{array} \right.$$ ​

Accepted Answer

A) ​ $\left( \frac { 3 } { 2 } , \frac { 1 } { 2 } \right)$ 
B) ​ $$\left( - \frac { 3 } { 2 } , \frac { 1 } { 2 } \right)$$ 
C) ​ $$\left( \frac { 3 } { 2 } , - \frac { 9 } { 2 } \right)$$ 
D) ​ $\left( - \frac { 3 } { 2 } , - \frac { 1 } { 2 } \right)$ 
E)  $\left( \frac { 3 } { 2 } , - \frac { 1 } { 2 } \right)$

Question 6

An airplane flying into a headwind travels 1128.00 miles in 4 hours and 42 minutes.On the return flight,the distance is traveled in 4 hours.Find the airspeed of the plane and the speed of the wind,assuming that both remain constant. ​

Accepted Answer

A) plane speed = 238 mph;wind speed = 250 mph 
B) plane speed = 276 mph;wind speed = 21.00 mph 
C) plane speed = 261.00 mph;wind speed = 21.00 mph 
D) plane speed = 238 mph;wind speed = 21.00 mph 
E) plane speed = 276 mph;wind speed = 268 mph

Question 7

A total of $32,000 is invested in two municipal bonds that pay 5.75% and 6.25% simple interest.The investor wants an annual interest income of $1,900 from the investments.What amount should be invested in the 5.75% bond? ​

Accepted Answer

A) $31,800 
B) $20,000 
C) $32,000 
D) $20,300 
E) $20,100

Question 8

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. ​​ $$\left\{ \begin{array} { c } 
x + y = 0 \
9 x + 8 y = 1
\end{array} \right.$$ ​​

Accepted Answer

A) ​(1,-1)​  
B) ​(0,1)​ ​  
C) ​(-1,1)​ ​  
D) ​(1,1)​ ​  
E) ​(-1,-1)​  ​

Question 9

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically. ​​ $$\left\{ \begin{array} { c } 
5 x + 7 y = 21 \
- 14 x - 18 y = - 38
\end{array} \right.$$ ​

Accepted Answer

A) ​(14,13) 
B) (-14,-13) ​ 
C) (-14,14) 
D) (-14,13) 
E) (14,-13)

Question 10

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. ​​ $$\left\{ \begin{array} { c } 
5 x - y = - 5 \
10 x + 3 y = - 10
\end{array} \right.$$ ​

Accepted Answer

A) (-1,0)​ ​
​  
B) ​(0,1) ​
​  
C) (10,1) ​
​  
D) ​(1,10)​  
E) ​(1,0) ​
​

Question 11

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ $$\left\{ \begin{array} { l } 
x + 2 y = 6 \
x - 2 y = 2
\end{array} \right.$$ ​

Accepted Answer

A) ​(1,4) 
B) ​(4,1) 
C) (-​4,-1) 
D) (​4,-1) 
E) ​(1,-4)

Question 12

Sixty liters of a 43% acid solution is obtained by mixing a 28% solution with a 42% solution.Use a graphing utility to graph the two given equations.Let x and y represent the amounts of the 28 % solution and 42% solution.As the amount of the 28% solution increases,how does the amount of the 42% solution change? $$\left\{ \begin{array} { l } 
x + y = 60 \
0.28 x + 0.42 y = 25.8
\end{array} \right.$$ ​ ​
​

Accepted Answer

A) ​  ​
Increases 
B) ​  ​
Decreases 
C) ​  ​
Decreases 
D) ​  ​
Decreases 
E) ​ 
Increases

Question 13

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ $$\left\{ \begin{array} { l } 
4 b + 4 m = \frac { 156 } { 35 } \\
4 b + 11 m = \frac { 471 } { 35 }
\end{array} \right.$$ ​

Accepted Answer

A) ​ $$\left( \frac { 6 } { 35 } , \frac { 9 } { 7 } \right)$$ 
B)  $$\left( \frac { - 6 } { 35 } , \frac { 9 } { 7 } \right)$$ 
C) ​ $$\left( \frac { 9 } { 7 } , \frac { 6 } { 35 } \right)$$ 
D) ​ $$\left( \frac { 9 } { 7 } , \frac { - 6 } { 35 } \right)$$ 
E) ​ $$\left( \frac { - 9 } { 7 } , \frac { - 6 } { 35 } \right)$$

Question 14

Two cheeseburgers and one small order of French fries from a fast-food restaurant contain a total of 850 calories.Three cheeseburgers and two small orders of French fries contain a total of 1380 calories.Find the caloric content of each item. ​

Accepted Answer

A) Cheeseburger: 320 calories;French fries: 210 calories 
B) ​Cheeseburger: 210 calories;French fries: 320 calories 
C) ​Cheeseburger: 850 calories;French fries: 320 calories 
D) ​Cheeseburger: 210 calories;French fries: 210 calories 
E) ​Cheeseburger: 320 calories;French fries: 320 calories

Question 15

Seven hundred gallons of 87-octane gasoline is obtained by mixing 87-octane gasoline with 90-octane gasoline.Use a graphing utility to graph the two given equations.Let x and y represent the number of gallons of the 87-octane gasoline and 90-octane gasoline.As the number of gallons of the 87-octane gasoline increases,how does the number of gallons of the 90-octane gasoline change?​ $$\left\{ \begin{array} { l } 
x + y = 700 \
87 x + 90 y = 60,900
\end{array} \right.$$ ​

Accepted Answer

A) ​  Increases 
B) ​  Decreases 
C) ​  Decreases 
D) ​  Increases 
E) ​  Decreases

Question 16

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ $$\left\{ \begin{array} { r } 
x + 5 y = 11 \
3 x - 10 y = 18
\end{array} \right.$$ ​

Accepted Answer

A)  $\left( - 8 , \frac { 3 } { 5 } \right)$ ​ 
B)  $\left( - 8 , - \frac { 3 } { 5 } \right)$ ​ 
C)  $\left( 8 , \frac { 3 } { 5 } \right)$ ​ 
D)  $\left( 8 , - \frac { 3 } { 5 } \right)$ ​ 
E)  $\left( 8 , \frac { 5 } { 3 } \right)$ ​

Question 17

​Solve the system of linear equations using any method,find (x,y). ​​ $\left\{ \begin{array} { l } 
3 x + 8 y = 2 \
y = x - 5
\end{array} \right.$ ​

Accepted Answer

A) ​ $\left( \frac { 42 } { 11 } , - \frac { 13 } { 11 } \right)$ 
B) ​ $\left( \frac { 11 } { 42 } , \frac { 11 } { 26 } \right)$ 
C) ​ $\left( \frac { 42 } { 11 } , \frac { 26 } { 11 } \right)$ 
D) No solution 
E) ​ $\left( \frac { 84 } { 11 } , \frac { 78 } { 11 } \right)$

Question 18

Use any method to solve the system of linear equations,find (x,y). ​​ $$\left\{ \begin{array} { c } 
4 x - 3 y = 16 \
- 5 x + 3 y = - 23
\end{array} \right.$$ ​

Accepted Answer

A) (7,4) 
B) ​(4,7) 
C) ​​(4,-7) 
D) ​(-7,4) 
E) ​(-7,-4)

Question 19

​Solve the system of linear equations by the method of elimination,find (x,y). ​​ $$\left\{ \begin{array} { c } 
\frac { 9 } { 4 } x + \frac { 1 } { 4 } y = \frac { - 7 } { 4 } \
9 x + y = - 7
\end{array} \right.$$ ​

Accepted Answer

A) ​(4,-43) 
B) (a,-7 - 9a)​(infinitely many solutions) 
C) ​(2,-25) 
D) ​No solutions 
E) ​(8,-79)

Question 20

Solve the system of linear equations by the method of elimination.Find (u,v)and check your solution algebraically.​ $$\left\{ \begin{array} { l } 
5 u + 6 v = 28 \
3 u + 5 v = 20
\end{array} \right.$$ ​

Accepted Answer

A) ​ $\left( \frac { 7 } { 20 } , \frac { 7 } { 16 } \right)$ 
B)  $\left( - \frac { 20 } { 7 } , \frac { 16 } { 7 } \right)$ ​ 
C)  $\left( \frac { 20 } { 7 } , - \frac { 16 } { 7 } \right)$ ​ 
D)  $\left( - \frac { 20 } { 7 } , - \frac { 16 } { 7 } \right)$ ​ 
E)  $\left( \frac { 20 } { 7 } , \frac { 16 } { 7 } \right)$ ​

Exam 42: Two Variable Linear Systems

Solve the system of linear equations by the method of elimination,find (x,y) . $\left\{ \begin{array} { l } - 0.06 x + 0.01 y = 0.03 \\- 0.09 x - 0.04 y = 0.09\end{array} \right.$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { l } 3 x + 11 y = 12 \\- 2 x - 5 y = 6\end{array} \right.$

Solve the system of linear equations using any method,find (x,y) . $\left\{ \begin{array} { r } 9 x - 2 y = 1 \\- 3 x + 2 y = 7\end{array} \right.$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { c } 5 x + 3 y = 6 \\3 x - y = 5\end{array} \right.$

An airplane flying into a headwind travels 1128.00 miles in 4 hours and 42 minutes.On the return flight,the distance is traveled in 4 hours.Find the airspeed of the plane and the speed of the wind,assuming that both remain constant.

A total of $32,000 is invested in two municipal bonds that pay 5.75% and 6.25% simple interest.The investor wants an annual interest income of $1,900 from the investments.What amount should be invested in the 5.75% bond?

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. $\left\{ \begin{array} { c } x + y = 0 \\9 x + 8 y = 1\end{array} \right.$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { c } 5 x + 7 y = 21 \\- 14 x - 18 y = - 38\end{array} \right.$

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. $\left\{ \begin{array} { c } 5 x - y = - 5 \\10 x + 3 y = - 10\end{array} \right.$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { l } x + 2 y = 6 \\x - 2 y = 2\end{array} \right.$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { l } 4 b + 4 m = \frac { 156 } { 35 } \\\\4 b + 11 m = \frac { 471 } { 35 }\end{array} \right.$

Two cheeseburgers and one small order of French fries from a fast-food restaurant contain a total of 850 calories.Three cheeseburgers and two small orders of French fries contain a total of 1380 calories.Find the caloric content of each item.

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { r } x + 5 y = 11 \\3 x - 10 y = 18\end{array} \right.$

Solve the system of linear equations using any method,find (x,y) . $\left\{ \begin{array} { l } 3 x + 8 y = 2 \\y = x - 5\end{array} \right.$

Use any method to solve the system of linear equations,find (x,y) . $\left\{ \begin{array} { c } 4 x - 3 y = 16 \\- 5 x + 3 y = - 23\end{array} \right.$

Solve the system of linear equations by the method of elimination,find (x,y) . $\left\{ \begin{array} { c } \frac { 9 } { 4 } x + \frac { 1 } { 4 } y = \frac { - 7 } { 4 } \\9 x + y = - 7\end{array} \right.$

Solve the system of linear equations by the method of elimination.Find (u,v) and check your solution algebraically. $\left\{ \begin{array} { l } 5 u + 6 v = 28 \\3 u + 5 v = 20\end{array} \right.$

Exam 42: Two Variable Linear Systems

​Solve the system of linear equations by the method of elimination,find (x,y) . ​​ {−0.06x+0.01y=0.03−0.09x−0.04y=0.09\left\{ \begin{array} { l } - 0.06 x + 0.01 y = 0.03 \\- 0.09 x - 0.04 y = 0.09\end{array} \right.{−0.06x+0.01y=0.03−0.09x−0.04y=0.09​ ​

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically.​ {3x+11y=12−2x−5y=6\left\{ \begin{array} { l } 3 x + 11 y = 12 \\- 2 x - 5 y = 6\end{array} \right.{3x+11y=12−2x−5y=6​ ​

​Solve the system of linear equations using any method,find (x,y) . ​​ {9x−2y=1−3x+2y=7\left\{ \begin{array} { r } 9 x - 2 y = 1 \\- 3 x + 2 y = 7\end{array} \right.{9x−2y=1−3x+2y=7​ ​

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically.​ {5x+3y=63x−y=5\left\{ \begin{array} { c } 5 x + 3 y = 6 \\3 x - y = 5\end{array} \right.{5x+3y=63x−y=5​ ​

An airplane flying into a headwind travels 1128.00 miles in 4 hours and 42 minutes.On the return flight,the distance is traveled in 4 hours.Find the airspeed of the plane and the speed of the wind,assuming that both remain constant. ​

A total of $32,000 is invested in two municipal bonds that pay 5.75% and 6.25% simple interest.The investor wants an annual interest income of $1,900 from the investments.What amount should be invested in the 5.75% bond? ​

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. ​​ {x+y=09x+8y=1\left\{ \begin{array} { c } x + y = 0 \\9 x + 8 y = 1\end{array} \right.{x+y=09x+8y=1​ ​​

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. ​​ {5x+7y=21−14x−18y=−38\left\{ \begin{array} { c } 5 x + 7 y = 21 \\- 14 x - 18 y = - 38\end{array} \right.{5x+7y=21−14x−18y=−38​ ​

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. ​​ {5x−y=−510x+3y=−10\left\{ \begin{array} { c } 5 x - y = - 5 \\10 x + 3 y = - 10\end{array} \right.{5x−y=−510x+3y=−10​ ​

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically.​ {x+2y=6x−2y=2\left\{ \begin{array} { l } x + 2 y = 6 \\x - 2 y = 2\end{array} \right.{x+2y=6x−2y=2​ ​