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

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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

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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

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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

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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

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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

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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 7x + 3y + 4z = 29 → (­-)7x + 3y + 4z = 29 -4x ­- y =- ­23
B.	3x + 4y + 2z = 6 → 6x + 8y + 4z = 12 7x + 3y + 4z = 29 → (-­)7x + 3y + 4z = 29 -x + 5y = ­-17
C.	3x + 4y + 2z = 6 → 6x + 8y + 4z = 6 7x + 3y + 4z = 29 → (-­)7x + 3y + 4z = 2 -x + 5y =- ­23
D.	3x + 4y + 2z = 6 → 6x + 8y + 4z = 12 7x + 3y + 4z = 29 → (-­)7x + 3y + 4z = 29 -x + 8y = 41

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Complete the sentence.

A system of equations in 3 variables always has infinite solutions if _________.

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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.