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Mathematics 141 Practice quiz 7
Solving Systems of Equations
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[1] Complete the system of equations (below) so that the system has exactly one solution, namely (1,2) ; that is, x = 1 and y = 2.
There are many correct answers. Hint : Guess, and then replace x by 1, and   y by 2, and check and revise your guess.
 
x   +   y   =   1
x   +   y   =   1

[2] For the system of equations in the box below, check the statement which is true, and if there is only one solution, enter it?
 
  4 x   -   6 y   =     2
-6 x   +   9 y   =   -3
  (a) The above system has no solution (1 pt if true)
(b) The above system has more than one solution (1 pt if true)
(c) The above system has one solution (½ pt if true), namely   x = and   y = (½ pt if true)

[3] For the system of equations in the box below, check the statement which is true, and if there is only one solution, enter it?
 
   x   +     y   =   30
2 x   +   8 y   =   84
  (a) The above system has no solution (1 pt if true)
(b) The above system has more than one solution (1 pt if true)
(c) The above system has one solution (½ pt if true), namely   x = and   y = (½ pt if true)
[4] For the system of equations in the box below, check the statement which is true, and if there is only one solution, enter it?
 
3 x   -   2 y   =   8
2 x   +   3 y   =   1
  (a) The above system has no solution (1 pt if true)
(b) The above system has more than one solution (1 pt if true)
(c) The above system has one solution (½ pt if true), namely   x = and   y = (½ pt if true)
[5] For the system of equations in the box below, check the statement which is true, and if there is only one solution, enter it?
 
2 x   -   3 y +   3 z   =   4
3 x  +   5 y  -   2 z   =   2
2 x   -  4 y  +   3 z   =   1
  (a) The above system has no solution (1 pt if true)
(b) The above system has more than one solution (1 pt if true)
(c) The above system has one solution (½ pt if true), namely   x = ,   y = , and   z = (½ pt if true)
[6] For the system of equations in the box below, check the statement which is true, and if there is only one solution, enter it?
 
2 x   +     y   -      z   =   1
   x  +   2 y  +   2 z   =   2
4 x   +  5 y  +   3 z   =   3
  (a) The above system has no solution (1 pt if true)
(b) The above system has more than one solution (1 pt if true)
(c) The above system has one solution (½ pt if true), namely   x = ,   y = , and   z = (½ pt if true)
[7] Read the problem in the box below. You must answer part (a) correctly to get credit for part (b)
 
The crew for the spaceship ZETA must be chosen from aliens of 2 different species : Romulans and Webbans. Romulans have 2 hands and Webbans have 8 hands. If there are exactly 30 crew members, and the crew must have a total of exactly 84 hands , then how many aliens of each species must be chosen?
  (a) In answering the above question by algebra, how should we define variables x and   y ? (for ½ pt)
  (a) Let   x = Romulans and let   y = Webbans
(b) Let   x and   y = the number of hands in the crew
(c) Let   x and   y = the size of the crew
(d) Let   x and   y = how many aliens of each species which must be chosen
(e) Let   x = the number of Romulans and let   y = the number of Webbans in the crew
  (b)Translate the underlined words in the box above (for ½ pt) :
x   +   y   =  
[8] Read the problem in the box below. You must answer part (a) correctly to get credit for part (b)
 
In Jurassic Park, a T-Rex can gobble 5 humans per day, a Velociraptor can gobble 1 human per day, and ten minisaurs can cooperatively gobble one human per day. There are a total of 62 of these 3 species in Jurassic Park ; there are 5 times as many Velociraptors as T-Rexes. If 25 humans were gobbled today , and all the dinosaurs gobbled humans to their capacity, how many dinosaurs of each species lives in Jurassic Park?
  (a) In answering the above question by algebra, how should we define variables x and   y ? (for ½ pt)
  (a) Let   x , y and   z = the number of dinosaurs in Jurassic Park
(b) Let   x = the number of T-Rexes,   y = the number of Velociraptors, and   z = the number of Minisaurs in the Park
(c) Let   x = T-Rexes, let   y = Velociraptors, and let   z = minisaurs
(d) Let   x , y and   z = the number of humans gobbled today
(e) Let   x , y and   z = how many dinosaurs of each species there are in Jurassic Park
  (b)Translate the underlined words in the box above (for ½ pt) :
x   +   y +   z   =  
[9] The problem in the box below is the same as in problem [8] above, but different words are underlined. You must answer question [8a] correctly to get credit for question [9] here.
 
In Jurassic Park, a T-Rex can gobble 5 humans per day, a Velociraptor can gobble 1 human per day, and ten minisaurs can cooperatively gobble one human per day. There are a total of 62 of these 3 species in Jurassic Park ; there are 5 times as many Velociraptors as T-Rexes . If 25 humans were gobbled today , and all the dinosaurs gobbled humans to their capacity, how many dinosaurs of each species lives in Jurassic Park?
 
Translate the underlined words in the box above :
x   +   y +   z   =  
[10]
5 x   +   3 y             =   4
            3  y   - 4 z   =   0
    x              +   z     =   1




At the left, enter numbers (such as 3, 0, or -2) to create the first matrix used in solving the above system by the Gauss-Jordan method
At the right, enter numbers (such as 3, 0, or -2) to complete the last matrix used in solving the above system by the Gauss-Jordan method

0
0		 0

0		 0
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