2. Solve the system of equations. 1
ży 22
—1
x + 3y = 2 = 10
11/x + 2
+ z = -4

9514 1404 393

  (x, y, z) = (2, 1, -5)

Step-by-step explanation:

There are numerous equation solvers available on the web. The attached result is from one of them.

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You may find it easier to solve these by hand if you eliminate fractions.

The first step is to look to see what you have, then formulate a strategy for getting a solution. Because the equations containing y have opposite coefficients, one of which is -1, we choose to use those to eliminate y. Immediately, we will have two equations in x and z.

If  you multiply the first equation by 3 and add that to the second, then you will eliminate y. The third equation already has y eliminated, so you will then have two equations in x and z.

  3(2x -y +z) +(x +3y -z) = 3(-2) +(10)

  6x -3y +3z +x +3y -z = -6 +10

  7x +2z = 4 . . . . [eq4]

Subtracting the third equation from this eliminates z, so you have ...

  (7x +2z) -(x +2z) = (4) -(-8)

  6x = 12

  x = 2

Substituting into the third equation gives ...

  2 +2z = -8

  2z = -10

  z = -5

Then using the first equation, you have ...

  y = 2x +z +2 = 2(2) +(-5) +2 = 1

(x, y, z) = (2, 1, -5)