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Solve the system of equations by substitution.\newline2x+3y−z=172x + 3y - z = 17\newline−2x−2y−2z=−14-2x - 2y - 2z = -14\newlinez=2z = 2

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Q. Solve the system of equations by substitution.\newline2x+3y−z=172x + 3y - z = 17\newline−2x−2y−2z=−14-2x - 2y - 2z = -14\newlinez=2z = 2
  1. Substitute z=2z = 2: First, let's substitute z=2z = 2 into the first two equations.\newline2x+3y−(2)=172x + 3y - (2) = 17\newline−2x−2y−2(2)=−14-2x - 2y - 2(2) = -14
  2. Simplify equations: Now, simplify the equations.\newline2x+3y−2=172x + 3y - 2 = 17\newline−2x−2y−4=−14-2x - 2y - 4 = -14
  3. Add constants: Add 22 and 44 to both sides of the respective equations.\newline2x+3y=192x + 3y = 19\newline−2x−2y=−10-2x - 2y = -10
  4. Eliminate x: Now, let's add the two equations together to eliminate x.\newline(2x+3y)+(−2x−2y)=19+(−10)(2x + 3y) + (-2x - 2y) = 19 + (-10)
  5. Combine like terms: Simplify the equation. 2x−2x+3y−2y=19−102x - 2x + 3y - 2y = 19 - 10
  6. Find yy: Combine like terms.y=9y = 9
  7. Substitute y=9y = 9: Now, substitute y=9y = 9 into one of the original equations to find xx.2x+3(9)−2=172x + 3(9) - 2 = 17
  8. Simplify equation: Simplify the equation. 2x+27−2=172x + 27 - 2 = 17
  9. Combine like terms: Combine like terms. 2x+25=172x + 25 = 17
  10. Subtract 2525: Subtract 2525 from both sides.\newline2x=17−252x = 17 - 25
  11. Calculate x: Calculate the value of x.\newline2x=−82x = -8\newlinex=−4x = -4

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