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Solve the system of equations by substitution.\newliney=−6y = -6\newline2x+y+z=−132x + y + z = -13\newline−x+2y−2z=−13-x + 2y - 2z = -13

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Q. Solve the system of equations by substitution.\newliney=−6y = -6\newline2x+y+z=−132x + y + z = -13\newline−x+2y−2z=−13-x + 2y - 2z = -13
  1. Calculate Rolls Needed: First, let's find out how many rolls the electrician needs by dividing the total amount of tape by the amount of tape on each roll. 8,000 cm÷2,000 cm/roll=4 rolls.8,000 \, \text{cm} \div 2,000 \, \text{cm}/\text{roll} = 4 \, \text{rolls}.
  2. Substitute yy into Equations: Since yy is already given as y=−6y = -6, we can substitute this value into the other two equations.
  3. Solve for zz: Substitute y=−6y = -6 into the second equation: 2x+(−6)+z=−13.2x + (-6) + z = -13.\newline2x−6+z=−13.2x - 6 + z = -13.
  4. Substitute yy into Third Equation: Now, let's solve for zz by adding 66 to both sides of the equation: 2x+z=−72x + z = -7.
  5. Solve for xx: Substitute y=−6y = -6 into the third equation: −x+2(−6)−2z=−13.-x + 2(-6) - 2z = -13.\newline−x−12−2z=−13.-x - 12 - 2z = -13.
  6. Correct Previous Mistake: Now, let's solve for xx by adding 1212 to both sides of the equation: −x−2z=−1-x - 2z = -1.
  7. Correct Previous Mistake: Now, let's solve for xx by adding 1212 to both sides of the equation: −x−2z=−1-x - 2z = -1.We made a mistake in the previous step; we should have added 1212 to both sides of the equation: −x−2z=−1+12-x - 2z = -1 + 12.\newline−x−2z=11-x - 2z = 11.

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