PRECAL II

Chapter 10 Test

Question 1 Solve the system of equations. x+ y=4 x−y=2

a. (1, 3) b. (– 1, 5) c. (3, 1) d. (5, – 1)

Question 2 Solve the system of equations. 2x+ 5y=19 7x−5y=−1

a. (2, 2) b. (2, 3) c. (3, 3) d. (3, 2)

Question 3 Solve the system of equations. x−y=−12

x−2y=−19 a. (– 5, 7) b. (– 6, 7) c. (– 5, 8) d. (– 6, 8)

Question 4 Solve the system of equations. x+ y−z=6

−x+ y−4z=9 2x+ y−z=9

a. (4, – 1, –2) b. (3, 0, – 2) c. (3, 0, – 3) d. No solution

Question 5 Solve the system of equations. 2x−5y+ 3z=10 2x−2y+ 3z=7

−4x+ 7y−6z=−16 a. (4, – 1, –1) b. (4, – 2, 0) c. (4, 0, – 2) d. No solution

Question 6 Bob invested $12,000, part at 2% and part at 11%. If the total interest at the end of the year is $870, how much did he invest at 2%?

a. $7,000 b. $6,000 c. $5,000 d. $4,000

Question 7 Solve the system using Gauss-Jordan elimination. x1+2x2=−11 3x1+x2=17

a. x1=9, x2=– 11 b. x1=10, x2=– 10 c. x1=9, x2=– 10 d. No solution

Question 8 Solve the system using Gauss-Jordan elimination. −9x1−3x2=51

3 x1+ x2=17

a. x1=3, x2=7 b. x1=4, x2=8 c. x1=3, x2=8 d. No solution

Question 9 Solve the system using Gauss-Jordan elimination.

−x1−x2+ x3=−7 x1+ x2+ 4 x3=−8 4x1+ x2+ x3=4

a. x1=1, x2=3, x3=– 3 b. x1=1,x2=3, x3=– 2 c. x1=2, x2=2, x3=– 2 d. No solution

Question 10 Solve the system using Gauss-Jordan elimination.

−x1+ x2+ 2 x3=2 2x1+ x2+ 5 x3=−4

8x1+ 4 x2+ 20 x3=−17

a. x1=– 3, x2=– 3, x3=1 b. x1=– 3, x2=– 3, x3=0 c. x1=– 3, x2=– 2, x3=0 d. No solution

Question 11 Solve the system using Gauss-Jordan elimination.

3 x1−9x2+ 2 x3=−7 −6x1+ 18 x2+ x3=−11 9x1−27 x2+ 5 x3=−16

a. x1=4, x2=1, x3=– 5 b. x1=3s+ 1, x2=s+ 2, x3=s , s any real number

c. x1=3s+ 1,x2=s, x3=–5, s any realnumber d. No solution

Question 12 Solve the system using Cramer's rule. x+ 2y=−10 x−4y=14

a. x=−2, y=−4 b. x=2, y=−4 c. x=−2, y=4 d. x=2, y=4

Question 13 Solve the system using Cramer's rule. 4x−3y=3 5x+2y=−1

a. x= 19 23,

y=−3 23

b. x= −3 23,

y= 19 23

c. x= −19 23,

y= 3 23

d. x= 3

23, y=−19

23

Question 14 Evaluate the following determinant using co-factors. [ −5 6 3 −1 −1 −6 −7 8 7 ]

a. 44 b. –44 c. 14 d. –14

Question 15 Solve the system using Cramer's rule. x+ 4y =−23

−2y + z = 17 −x + 2z = 17

a. x=−7, y=−4, z=9 b. x=9, y=2, z=21 c. x=−3, y=−5, z=7

d. x=1, y=−4, z=9

Question 16 Solve the system using Cramer's rule. 3y−z =1

x−2y−z =3 x−y + 5z =−5

a. x=− 2 19

, y=−25 19

, z=28 19

b. x=− 25 19

, y= 2 19

, z=− 2 19

c. x=− 25 19

, y=− 2 19

, z=28 19

d. x= 28 19

, y=− 2 19

, z=−25 19

Question 17 Use Cramer's rule to solve for x only. 2x+ 7y−5z=−4 5x−8y−6z=3 8x−6y+ 3z=30

a. x = 2 b. x = 0 c. x = 3 d. x = 5

Question 18 Use Cramer's rule to solve for y only. 3x+5y−5z=4

10x−3y−3z=−8 10x−5y+ 8z=−39

a. y = -3 b. y = -1 c. y = -2 d. y = -5