Question 1

Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { c } 
( - 5 , - 1,4 ) \
x + y + z = - 2 \
x - y + 3 z = 8 \
5 x + y + z = - 22
\end{array}$$

Accepted Answer

A) solution 
B) not a solution 
A) solution 
B) not a solution

Question 2

Solve the system of equations by substitution.
-3x + 2y = -4 5x = -20

Accepted Answer

A) (4, -4) 
B) (-4, -4) 
C) (-4, 4) 
D) (-4, 0) 
A) (4, -4) 
B) (-4, -4) 
C) (-4, 4) 
D) (-4, 0)

Question 3

Solve the system of linear equations using the elimination method.
-$$\begin{aligned}
7 x - 5 y - z & = 27 \
x - 8 y + 9 z & = 4 \
3 x + y + z & = 33
\end{aligned}$$

Accepted Answer

A) (8, 4, 5) 
B) (-8, 5, 16) 
C) (16, 5, -8) 
D) (8, 5, 4) 
A) (8, 4, 5) 
B) (-8, 5, 16) 
C) (16, 5, -8) 
D) (8, 5, 4)

Question 4

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y.
-8x - 5y = 3 -24x + 15y = -12

Accepted Answer

A) (3, 4) 
B) no solution 
C) (8, 3) $$\text { 
D)  } \left( \frac { 16 } { 9 } , - \frac { 10 } { 9 } \right)$$ 
A) (3, 4) 
B) no solution 
C) (8, 3) $$\text { 
D)  } \left( \frac { 16 } { 9 } , - \frac { 10 } { 9 } \right)$$

Question 5

Determine if the ordered pair is a solution to the given inequality.
-$$5 x - 6 y > - 9 ; ( 3,4 )$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 6

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered
triple involving variable z.
-$$\begin{array} { r r } 
5 x + 2 y + z & = - 11 \
2 x - 3 y - z & = 17 \
7 x - y & = 12
\end{array}$$

Accepted Answer

A)  $( - 2,0 , - 1 )$ 
B)  $( 1 , - 5,0 )$ 
C)  no solution 
D)  $( 0 , - 6,1 )$ 
A)  $( - 2,0 , - 1 )$ 
B)  $( 1 , - 5,0 )$ 
C)  no solution 
D)  $( 0 , - 6,1 )$

Determine if the given ordered triple is a solution of the system. - (-5,-1,4) x+y+z=-2 x-y+3z=8 5x+y+z=-22

Solve the system of equations by substitution. -3x + 2y = -4 5x = -20

Solve the system of linear equations using the elimination method. - 7x-5y-z =27 x-8y+9z =4 3x+y+z =33

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y. -8x - 5y = 3 -24x + 15y = -12

Determine if the ordered pair is a solution to the given inequality. - $5 x - 6 y > - 9 ; ( 3,4 )$

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z. - 5x+2y+z =-11 2x-3y-z =17 7x-y =12

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Exam 7: Systems of Equations and Inequalities