Answer:
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]
Values for x, y and z are:
[tex]x = 12[/tex]
[tex]y = 11[/tex]
[tex]z = 2[/tex]
