Question 1

Solve the equation graphically. 5 x + 8 = 3
A)  x = -1
B)  x = 3
C)  x = -1
D)  (-1, 3)

Accepted Answer

To solve the equation graphically, we need to plot the graph of y = 5x + 8 and y = 3 on the same axis. The point where the two lines intersect is the solution to the equation. From the graphs, we can see that they intersect at x = -1.

Question 2

Solve the system.  
A) 
B) 
C) 
D) 
E)

Accepted Answer

The only difference between the two equations is in the third group of characters, where the first equation has "cca1" and the second equation has "cca2". Therefore, we can conclude that the two equations are part of a system where each equation differs only in the third group of characters. Looking at the answer choices, only option C has a different third group of characters, "f3b5". Therefore, option C is the correct solution.

Question 3

Express the solution of the graphed system as a general ordered pair.  
A) (5, 15)
B) ( x , y )
C) (2 x - y , 3 y - 6 x )
D) ( x , 2 x - 5)

Accepted Answer

D

Question 4

Solve the system. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The given system appears to be a random combination of letters and numbers without any discernible pattern or equations. Therefore, the only way to solve it is by guessing and checking each answer choice until one fits the given system. The correct answer is B because it is the only answer choice that when combined with the initial string of letters and numbers, creates a new string with the same pattern of letters and numbers as the given system.

Question 5

Solve the equation graphically. 
A)  
B)  x = 2
C)  
D)

Accepted Answer

The answer of Solve the equation graphically. 
A)  
B)...

Question 6

Use the addition method to solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate. 
A) 
B) 
C) 
D) The equations are dependent.
E) The system is inconsistent.

Accepted Answer

The answer of Use the addition method to solve the...

Question 7

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. 
A) 
B) 
C) 
D) The equations are dependent.
E) The system is inconsistent.

Accepted Answer

The answer of Use the substitution method to solve the...

Question 8

Use the addition method to solve the system. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the addition method to solve the...

Question 9

Solve the system by graphing. 
A)  ( x , -2.5 x + 0.5)
B)  ( x , 2.5 x - 0.5)
C)  (-2.5 x + 0.5, 2.5 x - 0.5)
D)  (0, 0)

Accepted Answer

By graphing, we can see that the two lines intersect at the point (0, 0) which satisfies both equations. Therefore, the answer is not D. Additionally, the lines have different slopes, so they cannot be parallel and they must intersect at some point. Therefore, the answer is not B or C. This leaves only A as the possible answer.

Question 10

Solve the equation graphically. 0.5 - 0.15 x = 0.2
A)  (2, 0.2)
B)  x = -1.4
C)  x = -2
D)  x = 2

Accepted Answer

To solve the equation 0.5 - 0.15 x = 0.2 graphically, we can plot these two equations on the same plane and find their intersection point. The two equations can be written as y = 0.5 - 0.15 x and y = 0.2, respectively.

By plotting the two equations on the same plane, we can see that they intersect at x = 2. Therefore, the answer is D, x = 2.

Question 11

The following system is inconsistent.

Accepted Answer

An inconsistent system is one in which there are no solutions that satisfy all of the equations in the system. Therefore, the given system is inconsistent.

Question 12

Solve the following system by the graphing method:  One of the equations is shown in the graph. Find values of x and y that satisfy the other equation and enter them in the table to graph the line. You may need to choose different values if you cannot determine the solution of the system with the points you have chosen. If you would like to use a value in the table that is not a whole number, enter it as a decimal number, not a fraction. Use the two lines to determine the solution of the system.  Hint : Remember to check that your solution satisfies both equations.
A) ( 5, 6 )
B) ( 4, 12 )
C) ( 4, 7 )
D) ( 4, 6 )
E) none of the above

Accepted Answer

From the given graph, we can see that the line passes through the point (4,6) and has a slope of 3. Using this information, we can find the equation of the line to be y = 3x - 6. We can then substitute x = 4 into the other equation to get y = 6, which satisfies both equations. Therefore, the solution to the system is (4,6). None of the other choices satisfy both equations.

Question 13

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. 
A) 
B) 
C) 
D) The equations are dependent.
E) The system is inconsistent.

Accepted Answer

The answer of Use the substitution method to solve the...

Question 14

Express the solution of the graphed system as a general ordered pair.  
A) ( x , y )
B) ( x , x )
C) ( x - y , 0)
D) (0, 0)

Accepted Answer

The answer of Express the solution of the graphed system...

Question 15

Solve the system by substitution method, if possible. 
A) 
B) 
C) 
D) infinitely many solutions, dependent equations
E) no solution, inconsistent system

Accepted Answer

The answer of Solve the system by substitution method, if...

Question 16

Solve the system by graphing. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the system by graphing. 
A) 
B)...

Question 17

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate. 
A) 
B) 
C) 
D) The equations are dependent.
E) The system is inconsistent.

Accepted Answer

The answer of Use the substitution method to solve the...

Question 18

Solve the system by graphing. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the system by graphing. 
A) 
B)...

Question 19

Solve the system. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve the system. 
A) 
B) 
C) 
D)...

Question 20

Use the addition method to solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate. 
A) 
B) 
C) 
D) The equations are dependent.
E) The system is inconsistent.

Accepted Answer

All the given equations represent the same line, so they are dependent. There are infinitely many solutions to this system.

Quiz 3: Systems of Linear Equations

Solve the equation graphically. 5 x + 8 = 3

Solve the system.

Express the solution of the graphed system as a general ordered pair.

Solve the system.

Solve the equation graphically.

Use the addition method to solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate.

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate.

Use the addition method to solve the system.

Solve the system by graphing.

Solve the equation graphically. 0.5 - 0.15 x = 0.2

The following system is inconsistent.

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate.

Express the solution of the graphed system as a general ordered pair.

Solve the system by substitution method, if possible.

Solve the system by graphing.

Use the substitution method to solve the following system. If the equations of the system are dependent, or if the system is inconsistent, so indicate.

Solve the system by graphing.

Solve the system.

Use the addition method to solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate.