SOLUTION: Find the value of z in the system equations 2x + 3y - 5z = 3 x - 2y + z = 0 3x + y + 3z = 7 using Cramer's rule. answers(0,4/7,1,10/7) Find the value of x in the system of e

Find the value of z in the system equations
2x + 3y - 5z = 3
x - 2y + z = 0
3x + y + 3z = 7
using Cramer's rule. answers(0,4/7,1,10/7)

Write the single letters x, y, and z as
1x, 1y, and 1z, so that like terms in the
three equations all line up vertically:

2x + 3y - 5z = 3
1x - 2y + 1z = 0
3x + 1y + 3z = 7

Form the determinant D by erasing everything
but the coefficients of the letters:

2  + 3  - 5     
1  - 2  + 1 
3  + 1  + 3     

Erase the + signs and move the - signs 
closer to the numbers:

2    3   -5     
1   -2    1 
3    1    3

Then put vertical bars around it:

    |2    3   -5|     
D = |1   -2    1| 
    |3    1    3|

Do you know how to find the value of a 3x3 determinant?
I'll assume you do and can find that D = -49.

Now we want to find z, which is the 3rd unknown in the
system, going left to right.  Since it is the 3rd unknown,
we form Dz by replacing the 3rd column of D, which is

-5
 1
 3

by the column of constants, which is 

3
0
7

getting

     |2    3    3|     
Dz = |1   -2    0| 
     |3    1    7|
 
and we expand that determinant, getting

Dz = -28


        Dz     -28
So z = ———— = ————— =  
         D     -49

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Find the value of x in the system of equations
2x + y - 4 = 0
13x + (5/2)y - 10 = 0
using Cramer's rule. (-2,-1,0,1)

Write the single letter y as 1y.

2x + 1y - 4 = 0
13x + (5/2)y - 10 = 0

Then get all the letter terms on the left and 
all the number terms on the right, so that like 
terms in the three equations all line up 
vertically:

 2x + 1y = 4
13x - y = 10

Form the determinant D by erasing everything
but the coefficients of the letters:

 2    1       
13  -       

Erase the + signs and move the - sign 
closer to the number:

 2   1       
13  -


Then put vertical bars around it:

| 2   1|       
|13  -|

Do you know how to find the value of a 2x2 determinant?
I'll assume you do and can find that D = -18.

Now we want to find x, which is the 1st unknown in the
system, going left to right.  Since it is the 1st unknown,
we form Dx by replacing the 1st column of D, which is

 2
13

by the column of constants, which is

 4
10

 getting

Dx = | 4   1|       
     |10  -|
 
and we expand that determinant, getting

Dx = -20
        Dx     -20
So x = ———— = ————— =  
         D     -18

That's not one of your choices, but it
IS correct anyway.  The whole solution
is

x = 10/9,  y = 16/9

2x + 1y - 4 = 0
13x + y - 10 = 0

2 +  - 4 = 0
13 +  - 10 = 0

 +  - 4 = 0
 +  - 4 = 0



Find the value of y in the system equations
5x - 3y = 18
2x + 4y = 2
using Cramer's rule. (-2,-1,0,1)

Find the value of y in the system of equations
2x + 3y - 5z = 3
x - 2y + z = 0
3x + y + 3z = 7
using Cramer's rule 
(0,4/7,1,10/7)