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Solve the system of equations by substitution.\newline−x−2y−2z=3-x - 2y - 2z = 3\newline3x+2y+z=−123x + 2y + z = -12\newlinez=7z = 7

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Q. Solve the system of equations by substitution.\newline−x−2y−2z=3-x - 2y - 2z = 3\newline3x+2y+z=−123x + 2y + z = -12\newlinez=7z = 7
  1. Substitute z=7z = 7: Substitute z=7z = 7 into the first equation −x−2y−2z=3-x - 2y - 2z = 3.
    −x−2y−2×7=3-x - 2y - 2\times7 = 3
    −x−2y−14=3-x - 2y - 14 = 3
    −x−2y=17-x - 2y = 17
  2. Solve for x: Now, let's solve for x.\newlinex=−2y−17x = -2y - 17
  3. Substitute z=7z = 7: Substitute z=7z = 7 into the second equation 3x+2y+z=−123x + 2y + z = -12.\newline3x+2y+7=−123x + 2y + 7 = -12\newline3x+2y=−193x + 2y = -19
  4. Solve for yy: Now substitute xx from the first modified equation into the second modified equation.3(−2y−17)+2y=−193(-2y - 17) + 2y = -19−6y−51+2y=−19-6y - 51 + 2y = -19−4y−51=−19-4y - 51 = -19
  5. Find xx: Solve for yy.−4y=32-4y = 32y=−8y = -8
  6. Final Solution: Now we have yy, let's find xx using x=−2y−17x = -2y - 17.
    x=−2(−8)−17x = -2(-8) - 17
    x=16−17x = 16 - 17
    x=−1x = -1
  7. Final Solution: Now we have yy, let's find xx using x=−2y−17x = -2y - 17.
    x=−2(−8)−17x = -2(-8) - 17
    x=16−17x = 16 - 17
    x=−1x = -1We have xx and yy, and we know z=7z = 7 from the start.
    So the solution is (x,y,z)=(−1,−8,7)(x, y, z) = (-1, -8, 7).

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