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bogdanovich [222]
3 years ago
15

Solve the 3x3 system shown below. Enter the values of x, y, and z.

Mathematics
1 answer:
slamgirl [31]3 years ago
7 0

Answer:

x = 1

y = -1

z = 2

Step-by-step explanation:

You have the following system of equations:

x+2y-z=-3\ \ \ \ \ (1)\\\\2x-y+z=5\ \ \ \ \ \ (2)\\\\x-y+z=4\ \ \ \ \ (3)

First, you can subtract euqation (3) to equation (1):

x + 2y - z = -3

<u>-x +y  -z = - 4 </u>

0   3y  -2z = -7    (4)

Next, you can multiply equation (3) by 2 and subtract it to equation (2):

2[ x -y + z = 4]

<u> -2x +y -z = -5</u>

  0 -y + z= 3     (5)

You multiply equation (5) by 2 and sum (5) with (4):

2[ -y  + z = 3]

<u>    3y  -2z= -7</u>

  y  + 0 = -1

Then y = -1

Next, you replace y=-1 in (5) to obtain z:

-(-1) + z = 3

z = 2

Finally, you can replace z and y in the equation (3) to obtain x:

x - (-1) + (2) = 4

x = 1

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