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A. x = 12, y = 11, z = 2

Step-by-step explanation:

$$x + y + z = 25$$

$$5x + y + 9z = 89$$

$$- 7x + 6y + 6z = - 6$$

- Solve explicitly for 2 variables then substitute them into the third equation. Solving for x and z is a bit easier in this case.

$$x = 25 - y - z$$

- Substitute this in 5x + y + 9a = 89 then solve for z

$$5(25 - y - z) + y + 9z = 89$$

$$- 5y + y - 5z + 9z = 89 - 125$$

$$4z - 4y = - 36$$

$$\frac{4z - 4y}{4} = \frac{ - 36}{4}$$

$$z = y - 9$$

- Substitute both x and z into the third equation

$$- 7(25 - y - (y - 9)) + 6y + 6(y - 9) = - 6$$

$$- 175 + 7y + 7y - 63 + 6y + 6y - 54 = - 6$$

$$26y - 292 = - 6$$

$$26y = 286$$

$$y = 11$$

- Find z then find x by substituting the values you found.

$$z = 11 - 9 = 2$$

$$x = 25 - 11 - 2 = 12$$

Valuesforx,yandzare:

$$x = 12$$

$$y = 11$$

$$z = 2$$
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