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

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Q. Solve the system of equations by substitution.\newline−2x+3y+2z=3-2x + 3y + 2z = 3\newline−x−2y−2z=−15-x - 2y - 2z = -15\newlinez=−5z = -5
  1. Substitute z=−5z = -5: Substitute z=−5z = -5 into the first equation −2x+3y+2z=3-2x + 3y + 2z = 3.
    −2x+3y+2(−5)=3-2x + 3y + 2(-5) = 3
    −2x+3y−10=3-2x + 3y - 10 = 3
    −2x+3y=13-2x + 3y = 13
  2. Substitute z=−5z = -5: Substitute z=−5z = -5 into the second equation −x−2y−2z=−15-x - 2y - 2z = -15.\newline−x−2y−2(−5)=−15-x - 2y - 2(-5) = -15\newline−x−2y+10=−15-x - 2y + 10 = -15\newline−x−2y=−25-x - 2y = -25
  3. Solve for x: Solve for x from the equation −x−2y=−25-x - 2y = -25.−x=−25+2y-x = -25 + 2yx=25−2yx = 25 - 2y
  4. Substitute x=25−2yx = 25 - 2y: Substitute x=25−2yx = 25 - 2y into −2x+3y=13-2x + 3y = 13.
    −2(25−2y)+3y=13-2(25 - 2y) + 3y = 13
    −50+4y+3y=13-50 + 4y + 3y = 13
    7y−50=137y - 50 = 13
    7y=637y = 63
    y=9y = 9
  5. Substitute y=9y = 9: Substitute y=9y = 9 into x=25−2yx = 25 - 2y to find xx.\newlinex=25−2(9)x = 25 - 2(9)\newlinex=25−18x = 25 - 18\newlinex=7x = 7

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