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Solve the system of equations by substitution.\newline3x+3y+3z=123x + 3y + 3z = 12\newlinez=5z = 5\newline3x+2y−3z=−153x + 2y - 3z = -15

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Q. Solve the system of equations by substitution.\newline3x+3y+3z=123x + 3y + 3z = 12\newlinez=5z = 5\newline3x+2y−3z=−153x + 2y - 3z = -15
  1. Substitute z=5z = 5: Substitute z=5z = 5 into 3x+3y+3z=123x + 3y + 3z = 12.3x+3y+3⋅5=123x + 3y + 3\cdot5 = 123x+3y+15=123x + 3y + 15 = 123x+3y=−33x + 3y = -3
  2. Divide by 33: Divide the equation 3x+3y=−33x + 3y = -3 by 33 to simplify.\newlinex+y=−1x + y = -1
  3. Substitute z=5z = 5: Substitute z=5z = 5 into 3x+2y−3z=−153x + 2y - 3z = -15.\newline3x+2y−3×5=−153x + 2y - 3\times5 = -15\newline3x+2y−15=−153x + 2y - 15 = -15\newline3x+2y=03x + 2y = 0
  4. Solve for x: Now we have two equations:\newlinex+y=−1x + y = -1\newline3x+2y=03x + 2y = 0\newlineLet's solve for y using the first equation.\newlinex=−1−yx = -1 - y
  5. Substitute x=−1−yx = -1 - y: Substitute x=−1−yx = -1 - y into 3x+2y=03x + 2y = 0.\newline3(−1−y)+2y=03(-1 - y) + 2y = 0\newline−3−3y+2y=0-3 - 3y + 2y = 0\newline−3−y=0-3 - y = 0
  6. Solve for y: Solve for y.\newline−3−y=0-3 - y = 0\newline−y=3-y = 3\newliney=−3y = -3
  7. Substitute y=−3y = -3: Substitute y=−3y = -3 into x+y=−1x + y = -1.x−3=−1x - 3 = -1x=−1+3x = -1 + 3x=2x = 2

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