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Please help …. (x,y,z) in the boxes in the simplest terms

Please help …. (x,y,z) in the boxes in the simplest terms-example-1
User Hruske
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1 Answer

19 votes
19 votes

Answer:

(1, 1, 3)

Step-by-step explanation:

The initial system of equations is:

-2x + 3y - z = -2

3x + y = 4

-2y + 2z = 4

First, multiply the second equation by -1, so:

3x + y = 4

(-1)3x + (-1)y = (-1)4

- 3x - y = 4

Then, add this equation to the other two:

-2x + 3y - z = -2

- 3x - y = -4

-2y + 2z = 4

-5x + 0 + z = -2

-5x + z = -2

Now, let's solve for y and z as follows:

3x + y = 4

3x + y - 3x = 4 - 3x

y = 4 - 3x

-5x + z = -2

-5x + z + 5x = -2 + 5x

z = -2 + 5x

Finally, replace y = 4 - 3x and z = -2 + 5x in the first equation and solve for x

-2x + 3y - z = -2

-2x + 3(4 - 3x) - (-2 + 5x) = -2

-2x + 3(4) + 3(-3x) + 2 - 5x = -2

-2x + 12 - 9x + 2 - 5x = -2

-16x + 14 = -2

-16x + 14 - 14 = -2 - 14

-16x = -16

-16x/(-16) = -16/(-16)

x = 1

Now, with the value of x, we can calculate y and z as follows

y = 4 - 3x

y = 4 - 3(1)

y = 4 - 3

y = 1

z = -2 + 5x

z = -2 + 5(1)

z = -2 + 5

z = 3

Therefore, the answer in the form (x, y, z) is:

(1, 1, 3)

User Mattdwen
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