Solve the system of equations 3x - 4y +z=39, -3x + y -2z=-30, 2x -2y + 3z=43

x = 2, y = -6, and z = 9

Step-by-step explanation:

This question can be solved using multiple ways. I will use the Gauss Jordan Method.

Step 1: Convert the system into the augmented matrix form:

•  3  -4   1      |  39

•  -3   1  -2     |  -30

•  2  -2  3      |  43

Step 2: Add row 1 it into row 2:

•  3-4   1|  39

•  0  -3  -1|   9

•  2-2  3|  43

Step 3: Multiply row 1 with -2/3 and add it in row 3 and then multiply row 3 with 3:

•  3-4   1   |  39

•  0  -3  -1   |   9

•  0  2    7  |  51

Step 4: Multiply row 2 with 2/3 and add it in row 3 and then multiply row 3 with 3:

•  3-4     1       |  39

•  0-3    -1       |   9

•  00   19/3     |  57

Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

•3x - 4y + z = 39  

•-3y - z = 9

•(19/3)z = 57 (This implies that z = 9.)

Step 6: Since we have calculated z = 9, put this value in equation 2:

•-3y - 9 = 9

•-3y = 18

•y = -6.

Step 8: Put z = 9 and y = -6 in equation 1:

•3x - 4(-6) + 9 = 39

•3x + 24 + 9 = 39

•3x = 6.

•x = 2.

So final answer is x = 2, y = -6, and z = 9!!!

the camry sales+accord sale=828,000. to make it so the two numbers are 18 thousand apart and still equal 828,000, you first need to find out what half of 828,000 is. 828,000/2=414,000. for the two numbers to equal 828,000, you have to add the same amount as you subtract from the middle. in this case, the number is 9,000 because it's half of 18,000. to equal 828,000, you have to add 9,000 to 414,000 for the camry and subtract 9,000 from 414,000 for the accord. 414,000+9,000=423,000.

414,000-9,000=405,000.

423,000+405,000=828,000.

423,000-405,000=18,

hope it