Questions: Substitute the value of C obtained in Part (a), distribute it to all terms in the first equation, and add the equations together. c(2x+8y = -16) 3x+(-18)y = -4/(0x+αy) Enter the value of α, the coefficient of the y term. α =

Substitute the value of C obtained in Part (a), distribute it to all terms in the first equation, and add the equations together.

c(2x+8y = -16)
3x+(-18)y = -4/(0x+αy)

Enter the value of α, the coefficient of the y term.

α =

Transcript text: Substitute the value of $\mathcal{C}$ obtained in Part (a), distribute it to all terms in the first equation, and add the equations together. \[ \begin{aligned} c(2 x+8 y & =-16) \\ 3 x+(-18) y & =\frac{-4}{0 x+\alpha y} \end{aligned} \] Enter the value of $\alpha$, the coefficient of the $y$ term. \[ \alpha=\square \]

Solution

Solution Steps

Step 1: Identify the Value of $ C $

From the given information, we have: \[ C = -1.5 \]

Step 2: Substitute and Distribute

Substitute $ C = -1.5 $ into the first equation: \[ c(2x + 8y = -16) \] This becomes: \[ -1.5(2x + 8y) = -1.5 \times -16 \] Distribute $-1.5$ across the terms: \[ -3x - 12y = 24 \]

Step 3: Add the Equations

Now, add the distributed equation to the second equation: \[ \begin{aligned} -3x - 12y &= 24 \\ 3x - 18y &= \frac{-4}{0x + \alpha y} \end{aligned} \]

Step 4: Solve for $\alpha$

To find $\alpha$, we need to ensure the equations are consistent. The second equation simplifies to: \[ 3x - 18y = \frac{-4}{\alpha y} \] For the equation to be valid, the denominator must not be zero, and the equation must be consistent with the first. Solving for $\alpha$ involves ensuring the terms align correctly. However, the problem does not provide enough information to solve for $\alpha$ directly without additional context or constraints.