systems of equations math homework help
A student is solving the system of equations below. In which line is a mistake first made?
2x + y  2z = 23
3x + 2y + z = 11
x  y + z = 2
Line 1 z = 11 + 3x + 2y
Line 2 2x + y  2(11 + 3x + 2y) = 23
Line 3 4x  3y = 45
Line 4 x  y + (11 + 3x + 2y) =  2
Line 5 4x + y = – 13
Line 6 2y = 32
Line 7 y = 16, x = ¾, z = 11/4
a. Line 1
b. Line 3
c. Line 5
d. Line 6
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What is the solution to the system of equations shown below?
2x + 5y + 3z = 10
3x – y + 4z = 8
5x – 2y + 7z = 12
a. (7, 1, 3)
b. (7, 1, 3)
c. (7, 1, 3)
d. (7, 1, 3)
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Which ordered triple represents all of the solutions to the system of equations shown below?
2x  2y  z = 6
x + y + 3z = 3
3x  3y + 2z = 9
a. (x, x + 2, 0)
b. (x, x  3, 0)
c. (x + 2, x, 0)
d. (0, y, y + 4)
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What is the solution to the system of equations shown below?
2x  y + z = 4
4x  2y + 2z = 8
x + 3y  z = 5
a. (5, 4, 2)
b. (0, 5, 1)
c. No Solution
d. Infinite Solutions
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What is the solution to the system of equations shown below?
2x + y  3z = 11
x + 2y + 4z = 3
x  5y + 2z =  18
a. (1, 1, 4)
b. (1, 3, 2)
c. (3, 8, 1)
d. (2, 3, 0)
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A student is solving the system of equations below. What would be best next step in order to solve the system?
3x + y + z = 4
2x + 2y + 3z = 3
x + 3y + 2z = 5
A.  3x + y + z = 4 x + 3y + 2z = 5 
→  6x + 2y + 2z = 8 ()x + 3y + 2z = 5 5x  1y = 3 
B.  3x + y + z = 4 2x + 2y + 3z = 3 
→  9x + 3y + 3z = 12 ()x + 3y + 2z = 5 8x +1z = 7 
C.  3x + y + z = 4 x + 3y + 2z = 5 
→  9x + 3y + 3z = 12 ()x + 3y + 2z = 5 8x + 1z = 17 
D.  x + y + z = 4 x + 3y + 2z = 5 
→  3x + y + z = 4 ()3x + 9y + 6z = 15 8y – 5z = 9 
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Which image shows a system of equations with infinite solutions?
A. 
B. 
C.

D. 
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What is the solution to the system of equations shown below?
x y + z = 0
5x + 3y  2z = 1
2x – y + 4z = 11
a. (0, 3, 3)
b. (2, 5, 3)
c. no solution
d. infinitely many solutions
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Which answer correctly shows the first step that can be used to correctly solve the
system of equations?
5x + 2y = 4
3x + 4y + 2z = 6
7x + 3y + 4z = 29
A. 
3x + 4y + 2z = 6 → 3x + 4y + 4z = 6 4x  y = 23 
B. 
3x + 4y + 2z = 6 → 6x + 8y + 4z = 12 x + 5y = 17 
C. 
3x + 4y + 2z = 6 → 6x + 8y + 4z = 6 x + 5y = 23 
D. 
3x + 4y + 2z = 6 → 6x + 8y + 4z = 12 x + 8y = 41 
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Complete the sentence.
A system of equations in 3 variables always has infinite solutions if _________.
a. the planes intersect in one point
b. the planes have no common point
c. the planes intersect in a line.
d. the planes are parallel.
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