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PLEASE HELP WITH THIS ‼️
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A. x = 12, y = 11, z = 2

Step-by-step explanation:

[tex]x + y + z = 25[/tex]

[tex]5x + y + 9z = 89[/tex]

[tex] - 7x + 6y + 6z = - 6[/tex]

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

[tex]x = 25 - y - z[/tex]

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

[tex]5(25 - y - z) + y + 9z = 89[/tex]

[tex] - 5y + y - 5z + 9z = 89 - 125[/tex]

[tex]4z - 4y = - 36[/tex]

[tex] \frac{4z - 4y}{4} = \frac{ - 36}{4} [/tex]

[tex]z = y - 9[/tex]

- Substitute both x and z into the third equation

[tex] - 7(25 - y - (y - 9)) + 6y + 6(y - 9) = - 6[/tex]

[tex] - 175 + 7y + 7y - 63 + 6y + 6y - 54 = - 6[/tex]

[tex]26y - 292 = - 6[/tex]

[tex]26y = 286[/tex]

[tex]y = 11[/tex]

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

[tex]z = 11 - 9 = 2[/tex]

[tex]x = 25 - 11 - 2 = 12[/tex]

Valuesforx,yandzare:

[tex]x = 12[/tex]

[tex]y = 11[/tex]

[tex]z = 2[/tex]
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