Questions: Using the elimination strategy, combine the first and third equations to eliminate the x variable. Write the resulting equation. 2x + y + 9z = -50 3x - 2y + 9z = -70 -x + y - 3z = 25 Now, combine the second and third equations to eliminate the x variable. Write the resulting equation.

Using the elimination strategy, combine the first and third equations to eliminate the \(x\) variable. Write the resulting equation. \[ \begin{array}{l} 2 x+y+9 z=-50 \\ 3 x-2 y+9 z=-70 \\ -x+y-3 z=25 \end{array} \]

Multiply the third equation by 2.

Multiplying the third equation \(-x + y - 3z = 25\) by 2 gives \(-2x + 2y - 6z = 50\).

Add the first equation to the modified third equation.

Adding the first equation \(2x + y + 9z = -50\) to the modified third equation \(-2x + 2y - 6z = 50\) gives: \(2x + y + 9z + (-2x + 2y - 6z) = -50 + 50\) \(3y + 3z = 0\)

\(\boxed{3y + 3z = 0}\)

Now, combine the second and third equations to eliminate the \(x\) variable. Write the resulting equation. \[ \begin{array}{l} 2 x+y+9 z=-50 \\ 3 x-2 y+9 z=-70 \\ -x+y-3 z=25 \end{array} \]

Multiply the third equation by 3.

Multiplying the third equation \(-x + y - 3z = 25\) by 3 gives \(-3x + 3y - 9z = 75\).

Add the second equation to the modified third equation.

Adding the second equation \(3x - 2y + 9z = -70\) to the modified third equation \(-3x + 3y - 9z = 75\) gives: \(3x - 2y + 9z + (-3x + 3y - 9z) = -70 + 75\) \(y = 5\)

\(\boxed{y = 5}\)

\(\boxed{3y + 3z = 0}\) \(\boxed{y = 5}\)