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Solve the system of equations by substitution.\newline3x+3y+2z=−23x + 3y + 2z = -2\newline−x+2y−z=11-x + 2y - z = 11\newliney=4y = 4

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Q. Solve the system of equations by substitution.\newline3x+3y+2z=−23x + 3y + 2z = -2\newline−x+2y−z=11-x + 2y - z = 11\newliney=4y = 4
  1. Solve for yy: First, let's solve for yy in the third equation, which is already given as y=4y = 4.
  2. Substitute y into equations: Now, substitute y=4y = 4 into the first and second equations.\newlineFor the first equation: 3x+3(4)+2z=−23x + 3(4) + 2z = -2, which simplifies to 3x+12+2z=−23x + 12 + 2z = -2.\newlineFor the second equation: −x+2(4)−z=11-x + 2(4) - z = 11, which simplifies to −x+8−z=11-x + 8 - z = 11.
  3. Solve for x or z in first equation: Next, let's solve the simplified first equation for xx or zz. Let's solve for xx: 3x+2z=−2−123x + 2z = -2 - 12, which simplifies to 3x+2z=−143x + 2z = -14.
  4. Solve for x or z in second equation: Now, let's solve the simplified second equation for xx or zz. Let's solve for xx: −x−z=11−8-x - z = 11 - 8, which simplifies to −x−z=3-x - z = 3.
  5. Express xx in terms of zz: We can now express xx in terms of zz from the second equation: −x=3+z-x = 3 + z, or x=−3−zx = -3 - z.
  6. Substitute xx into first equation: Substitute x=−3−zx = -3 - z into the first equation: 3(−3−z)+2z=−143(-3 - z) + 2z = -14. This simplifies to −9−3z+2z=−14-9 - 3z + 2z = -14.
  7. Combine like terms: Combine like terms: −9−z=−14-9 - z = -14.
  8. Solve for z: Now, solve for z: −z=−14+9-z = -14 + 9, which simplifies to −z=−5-z = -5.
  9. Find xx: Divide by −1-1 to get zz: z=5z = 5.
  10. Find xx: Divide by −1-1 to get zz: z=5z = 5.Substitute z=5z = 5 into x=−3−zx = -3 - z to find xx: x=−3−5x = -3 - 5, which simplifies to x=−8x = -8.

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