Worksheets For Beginning & Intermediate Algebra With Integrated Review
Worksheets For Beginning & Intermediate Algebra With Integrated Review
6th Edition
ISBN: 9780134584911
Author: Martin-Gay, Elayn
Publisher: PEARSON
Question
Chapter 4.4, Problem 28E
To determine

To Answer:

To solve the system of linear equations with three variables.

Expert Solution & Answer
Check Mark

Answer to Problem 28E

Solution:

The solution of given system is (6,12,4).

Explanation of Solution

1) Concept:

Step 1: Simplify and put all three equations in the form Ax+By+Cz=D, if needed.

Step 2: Use elimination method to eliminate any one of the variables. So that we get two equations with two unknowns.

Step 3: Solve the remaining system of equations just as solving a system of linear equations with two unknowns.

Step 4: Solve for the third variable.

Step 5: Check whether solved solutions satisfy the given system of equations by substituting the values obtained in the given system of linear equations.

2) Given:

13x14y+z=9(1)12x13y14z=6(2)x12yz=8(3)

Calculation:

From all the above three equations, we can observe that the coefficients of variables are in fractions.

To perform calculations easily, we can take L.C.M and make fraction as integers.

(I) Simplify all three equations

For simplifying (1) take L.C.M. By doing so, we get

13x14y+z=94x3y+12z12=94x3y+12z=108(1)

By simplifying (2), we get

12x13y14z=66x4y3z12=66x4y3z=12×66x4y3z=72(2)

Simplifying (3), we get

x12yz=82xy2z2=82xy2z=16(3)

Now the system of linear equations is

4x3y+12z=108(4)6x4y3z=72(5)2xy2z=16(6)

(II) We can choose to eliminate y

On multiplying (4) by 4 and (5) by 3 and by subtracting the resultant, we can eliminate y from equation (4) and (5)

Multiplying (3) by 4, we get

4(4x3y+12z)=10816x12y+48z=432,(7)

Multiplying (5) by 3, we get

3(6x4y3z)=7218x12y9z=216(8)

Subtracting (7) from (8), we get

16x12y+48z=43218x12y9z=2162x+57z=216¯(9)

By multiplying (6) by 4 and subtracting from (4), we can eliminate y from (5) and (6)

By multiplying (5) by 4, we get

4(2xy2z=16)8x4y8z=64(10)

Subtracting (5) from (10), we get

6x4y3z=728x4y8z=642x+5z=8(11)¯

Now we have two equations with two unknowns, the two equations are

2x+57z=216(9)2x+5z=8(11)

Solve for x and z

Subtracting (9) and (11), we get

2x+57z=2162x+5z=852z=208z=20852=4¯

Substitute z=4 in (11), we get

2x+5z=82x+5(4)=82x20=82x=12x=122=6x=6

III) Solve for third variable

Substitute x=6 and z=4 in (4), we get

4x3y+12z=1084(6)3y+12(4)=108243y48=1083y=108+48+243y=36y=363=12

IV) Verify:

Substitute x=6, y=12 and z=4 in (4), we get

4x3y+12z=1084(6)3(12)+12(4)=108243648=108108=108L.H.S=R.H.S

Conclusion:

(6,12,4) is the solution.

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Chapter 4 Solutions

Worksheets For Beginning & Intermediate Algebra With Integrated Review

Ch. 4.1 - Prob. 7PCh. 4.1 - Prob. 8PCh. 4.1 - Prob. 1VCh. 4.1 - Prob. 2VCh. 4.1 - Prob. 3VCh. 4.1 - Prob. 4VCh. 4.1 - Prob. 5VCh. 4.1 - Prob. 6VCh. 4.1 - Prob. 1ECh. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.1 - Prob. 6ECh. 4.1 - Prob. 7ECh. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.1 - Prob. 10ECh. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - Prob. 60ECh. 4.1 - Prob. 61ECh. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - Prob. 64ECh. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.1 - Prob. 67ECh. 4.1 - Prob. 68ECh. 4.1 - Prob. 69ECh. 4.1 - Prob. 70ECh. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - Prob. 73ECh. 4.1 - Prob. 74ECh. 4.1 - Prob. 75ECh. 4.1 - Prob. 76ECh. 4.1 - Prob. 77ECh. 4.1 - Prob. 78ECh. 4.2 - Prob. 1PCh. 4.2 - Prob. 2PCh. 4.2 - Prob. 3PCh. 4.2 - Prob. 4PCh. 4.2 - Prob. 5PCh. 4.2 - Prob. 6PCh. 4.2 - Prob. 1VCh. 4.2 - Prob. 2VCh. 4.2 - Prob. 3VCh. 4.2 - Prob. 4VCh. 4.2 - Prob. 5VCh. 4.2 - Prob. 6VCh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - Prob. 54ECh. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.2 - Prob. 57ECh. 4.2 - Prob. 58ECh. 4.3 - Prob. 1PCh. 4.3 - Prob. 2PCh. 4.3 - Prob. 3PCh. 4.3 - Prob. 4PCh. 4.3 - Prob. 5PCh. 4.3 - Prob. 6PCh. 4.3 - Prob. 1VCh. 4.3 - Prob. 2VCh. 4.3 - Prob. 3VCh. 4.3 - Prob. 4VCh. 4.3 - Prob. 1ECh. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - Prob. 31ECh. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Prob. 66ECh. 4.3 - Prob. 67ECh. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - Prob. 71ECh. 4.3 - Prob. 72ECh. 4.3 - Prob. 73ECh. 4.3 - Prob. 74ECh. 4.IR - Prob. 1IRCh. 4.IR - Prob. 2IRCh. 4.IR - Prob. 3IRCh. 4.IR - Prob. 4IRCh. 4.IR - Prob. 5IRCh. 4.IR - Prob. 6IRCh. 4.IR - Prob. 7IRCh. 4.IR - Prob. 8IRCh. 4.IR - Prob. 9IRCh. 4.IR - Prob. 10IRCh. 4.IR - Prob. 11IRCh. 4.IR - Prob. 12IRCh. 4.IR - Prob. 13IRCh. 4.IR - Prob. 14IRCh. 4.IR - Prob. 15IRCh. 4.IR - Prob. 16IRCh. 4.IR - Prob. 17IRCh. 4.IR - Prob. 18IRCh. 4.IR - Prob. 19IRCh. 4.IR - Prob. 20IRCh. 4.IR - Prob. 21IRCh. 4.IR - Prob. 22IRCh. 4.4 - Prob. 1PCh. 4.4 - Prob. 2PCh. 4.4 - Prob. 3PCh. 4.4 - Prob. 4PCh. 4.4 - Prob. 5PCh. 4.4 - Prob. 1VCh. 4.4 - Prob. 2VCh. 4.4 - Prob. 3VCh. 4.4 - Prob. 4VCh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Prob. 34ECh. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Prob. 44ECh. 4.4 - Prob. 45ECh. 4.4 - Prob. 46ECh. 4.5 - Prob. 1PCh. 4.5 - Prob. 2PCh. 4.5 - Prob. 3PCh. 4.5 - Prob. 4PCh. 4.5 - Prob. 5PCh. 4.5 - Prob. 6PCh. 4.5 - Prob. 7PCh. 4.5 - Prob. 8PCh. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Prob. 29ECh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Prob. 37ECh. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Prob. 41ECh. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - Prob. 49ECh. 4.5 - Prob. 50ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Prob. 53ECh. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - Prob. 57ECh. 4.5 - Prob. 58ECh. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Prob. 61ECh. 4.5 - Prob. 62ECh. 4.5 - Prob. 63ECh. 4.5 - Prob. 64ECh. 4.5 - Prob. 65ECh. 4.5 - Prob. 66ECh. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Prob. 69ECh. 4.5 - Prob. 70ECh. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 73ECh. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Prob. 76ECh. 4.5 - Prob. 77ECh. 4.5 - Prob. 78ECh. 4.5 - Prob. 79ECh. 4.5 - Prob. 80ECh. 4.5 - Prob. 81ECh. 4.5 - Prob. 82ECh. 4.5 - Prob. 83ECh. 4.5 - Prob. 84ECh. 4.5 - Prob. 85ECh. 4.5 - Prob. 86ECh. 4.VC - Prob. 1VCCh. 4.VC - Prob. 2VCCh. 4.VC - Prob. 3VCCh. 4.VC - Prob. 4VCCh. 4.VC - Prob. 5VCCh. 4.VC - Prob. 6VCCh. 4.VC - Prob. 7VCCh. 4.CR - Prob. 1CRCh. 4.CR - Prob. 2CRCh. 4.CR - Prob. 3CRCh. 4.CR - Prob. 4CRCh. 4.CR - Prob. 5CRCh. 4.CR - Prob. 6CRCh. 4.CR - Prob. 7CRCh. 4.CR - Prob. 8CRCh. 4.CR - Prob. 9CRCh. 4.CR - Prob. 10CRCh. 4.CR - Prob. 11CRCh. 4.CR - Prob. 12CRCh. 4.CR - Prob. 13CRCh. 4.CR - Prob. 14CRCh. 4.CR - Prob. 15CRCh. 4.CR - Prob. 16CRCh. 4.CR - Prob. 17CRCh. 4.CR - Prob. 18CRCh. 4.CR - Prob. 19CRCh. 4.CR - Prob. 20CRCh. 4.CR - Prob. 21CRCh. 4.CR - Prob. 22CRCh. 4.CR - Prob. 23CRCh. 4.CR - Prob. 24CRCh. 4.CR - Prob. 25CRCh. 4.CR - Prob. 26CRCh. 4.CR - Prob. 27CRCh. 4.CR - Prob. 28CRCh. 4.CR - Prob. 29CRCh. 4.CR - Prob. 30CRCh. 4.CR - Prob. 31CRCh. 4.CR - Prob. 32CRCh. 4.CR - Prob. 33CRCh. 4.CR - Prob. 34CRCh. 4.CR - Prob. 35CRCh. 4.CR - Prob. 36CRCh. 4.CR - Prob. 37CRCh. 4.CR - Prob. 38CRCh. 4.CR - Prob. 39CRCh. 4.CR - Prob. 40CRCh. 4.CR - Prob. 41CRCh. 4.CR - Prob. 42CRCh. 4.CR - Prob. 43CRCh. 4.CR - Prob. 44CRCh. 4.CR - Prob. 45CRCh. 4.CR - Prob. 46CRCh. 4.CR - Prob. 47CRCh. 4.CR - Prob. 48CRCh. 4.CR - Prob. 49CRCh. 4.CR - Prob. 50CRCh. 4.CR - Prob. 51CRCh. 4.CR - Prob. 52CRCh. 4.CR - Prob. 53CRCh. 4.CR - Prob. 54CRCh. 4.CR - Prob. 55CRCh. 4.CR - Prob. 56CRCh. 4.CR - Prob. 57CRCh. 4.CR - Prob. 58CRCh. 4.CR - Prob. 59CRCh. 4.CR - Prob. 60CRCh. 4.CR - Prob. 61CRCh. 4.CR - Prob. 62CRCh. 4.CR - Prob. 63CRCh. 4.GRT - Prob. 1GRTCh. 4.GRT - Prob. 2GRTCh. 4.GRT - Prob. 3GRTCh. 4.GRT - Prob. 4GRTCh. 4.GRT - Prob. 5GRTCh. 4.GRT - Prob. 6GRTCh. 4.GRT - Prob. 7GRTCh. 4.GRT - Prob. 8GRTCh. 4.GRT - Prob. 9GRTCh. 4.GRT - Prob. 10GRTCh. 4.GRT - Prob. 11GRTCh. 4.GRT - Prob. 12GRTCh. 4.CT - Prob. 1CTCh. 4.CT - Prob. 2CTCh. 4.CT - Prob. 3CTCh. 4.CT - Prob. 4CTCh. 4.CT - Prob. 5CTCh. 4.CT - Prob. 6CTCh. 4.CT - Prob. 7CTCh. 4.CT - Prob. 8CTCh. 4.CT - Prob. 9CTCh. 4.CT - Prob. 10CTCh. 4.CT - Prob. 11CTCh. 4.CT - Prob. 12CTCh. 4.CT - Prob. 13CTCh. 4.CT - Prob. 14CTCh. 4.CT - Prob. 15CTCh. 4.CT - Prob. 16CTCh. 4.CT - Prob. 17CTCh. 4.CT - Prob. 18CTCh. 4.CT - Prob. 19CTCh. 4.CT - Prob. 20CTCh. 4.CT - Prob. 21CTCh. 4.CM - Prob. 1CMCh. 4.CM - Prob. 2CMCh. 4.CM - Prob. 3CMCh. 4.CM - Prob. 4CMCh. 4.CM - Prob. 5CMCh. 4.CM - Prob. 6CMCh. 4.CM - Prob. 7CMCh. 4.CM - Prob. 8CMCh. 4.CM - Prob. 9CMCh. 4.CM - Prob. 10CMCh. 4.CM - Prob. 11CMCh. 4.CM - Prob. 12CMCh. 4.CM - Prob. 13CMCh. 4.CM - Prob. 14CMCh. 4.CM - Prob. 15CMCh. 4.CM - Prob. 16CMCh. 4.CM - Prob. 17CMCh. 4.CM - Prob. 18CMCh. 4.CM - Prob. 19CMCh. 4.CM - Prob. 20CMCh. 4.CM - Prob. 21CMCh. 4.CM - Prob. 22CMCh. 4.CM - Prob. 23CMCh. 4.CM - Prob. 24CMCh. 4.CM - Prob. 25CMCh. 4.CM - Prob. 26CMCh. 4.CM - Prob. 27CMCh. 4.CM - Prob. 28CMCh. 4.CM - Prob. 29CMCh. 4.CM - Prob. 30CMCh. 4.CM - Prob. 31CMCh. 4.CM - Prob. 32CMCh. 4.CM - Prob. 33CMCh. 4.CM - Prob. 34CMCh. 4.CM - Prob. 35CMCh. 4.CM - Prob. 36CMCh. 4.CM - Prob. 37CMCh. 4.CM - Prob. 38CMCh. 4.CM - Prob. 39CMCh. 4.CM - Prob. 40CMCh. 4.CM - Prob. 41CMCh. 4.CM - Prob. 42CMCh. 4.CM - Prob. 43CMCh. 4.CM - Prob. 44CM
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