Solve the system of equations by substitution. y = -6 2x + y + z = -13 -x + 2y - 2z = -13 ____

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.Substitute y into Equations: Since y is already given as y = -6, we can substitute this value into the other two equations.Solve for z: Substitute y = -6 into the second equation: 2x + (-6) + z = -13. 2x - 6 + z = -13.Substitute y into Third Equation: Now, let's solve for z by adding 6 to both sides of the equation: 2x + z = -7.Solve for x: Substitute y = -6 into the third equation: -x + 2(-6) - 2z = -13. -x - 12 - 2z = -13.Correct Previous Mistake: Now, let's solve for x by adding 12 to both sides of the equation: -x - 2z = -1.We made a mistake in the previous step; we should have added 12 to both sides of the equation: -x - 2z = -1 + 12. -x - 2z = 11.

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Solve the system of equations by substitution. $\newline$ $y = -6$ $\newline$ $2x + y + z = -13$ $\newline$ $-x + 2y - 2z = -13$

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Precalculus

Solve a system of equations in three variables using substitution

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Q. Solve the system of equations by substitution.

\newline

y = -6

\newline

2x + y + z = -13

\newline

-x + 2y - 2z = -13

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. $8,000 \, \text{cm} \div 2,000 \, \text{cm}/\text{roll} = 4 \, \text{rolls}.$
Substitute $y$ into Equations: Since $y$ is already given as $y = -6$ , we can substitute this value into the other two equations.
Solve for $z$ : Substitute $y = -6$ into the second equation: $2x + (-6) + z = -13.$ $\newline$ $2x - 6 + z = -13.$
Substitute $y$ into Third Equation: Now, let's solve for $z$ by adding $6$ to both sides of the equation: $2x + z = -7$ .
Solve for $x$ : Substitute $y = -6$ into the third equation: $-x + 2(-6) - 2z = -13.$ $\newline$ $-x - 12 - 2z = -13.$
Correct Previous Mistake: Now, let's solve for $x$ by adding $12$ to both sides of the equation: $-x - 2z = -1$ .
Correct Previous Mistake: Now, let's solve for $x$ by adding $12$ to both sides of the equation: $-x - 2z = -1$ .We made a mistake in the previous step; we should have added $12$ to both sides of the equation: $-x - 2z = -1 + 12$ . $\newline$ $-x - 2z = 11$ .