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Solve the system of equations by substitution.\newline−3x+2y+z=−6-3x + 2y + z = -6\newlinex−2y+2z=13x - 2y + 2z = 13\newlinex=7x = 7

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Q. Solve the system of equations by substitution.\newline−3x+2y+z=−6-3x + 2y + z = -6\newlinex−2y+2z=13x - 2y + 2z = 13\newlinex=7x = 7
  1. Substitute x=7x = 7: Substitute x=7x = 7 into the second equation x−2y+2z=13x - 2y + 2z = 13.\newline7−2y+2z=137 - 2y + 2z = 13
  2. Solve for z: Solve for z in terms of y.\newline2z=13+2y−72z = 13 + 2y - 7\newline2z=6+2y2z = 6 + 2y\newlinez=3+yz = 3 + y
  3. Substitute x=7x = 7 and z=3+yz = 3 + y: Substitute x=7x = 7 and z=3+yz = 3 + y into the first equation −3x+2y+z=−6-3x + 2y + z = -6.\newline−3(7)+2y+(3+y)=−6-3(7) + 2y + (3 + y) = -6\newline−21+2y+3+y=−6-21 + 2y + 3 + y = -6
  4. Combine and solve for yy: Combine like terms and solve for yy.3y−18=−63y - 18 = -63y=123y = 12y=4y = 4
  5. Substitute y=4y = 4: Substitute y=4y = 4 into z=3+yz = 3 + y to find zz.\newlinez=3+4z = 3 + 4\newlinez=7z = 7
  6. Final values of x, y, z: We have found the values for x, y, and z. x=7x = 7, y=4y = 4, z=7z = 7

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