Question

how can you eliminate the y - terms in this system? \\(\

$$\begin{cases}4x - 8y = 20 \\\\ 3x + 4y = 5\\end{cases}$$

\\) multiply by? on both sides.

Explanation:

Step1: Identify coefficients of y

The system is:
\( 4x - 8y = 20 \)
\( 3x + 4y = 5 \)
Coefficients of \( y \): \( -8 \) (first equation) and \( 4 \) (second equation).

Step2: Find multiplier for elimination

To eliminate \( y \), we need the coefficients of \( y \) to be opposites (or equal) when added. Multiply the second equation (\( 3x + 4y = 5 \)) by \( 2 \):
New second equation: \( 2(3x + 4y) = 2(5) \) → \( 6x + 8y = 10 \).

Now, add to first equation: \( (4x - 8y) + (6x + 8y) = 20 + 10 \), which eliminates \( y \).

Answer:

Multiply the equation \( 3x + 4y = 5 \) by \( 2 \) on both sides. So the multiplier is \( 2 \).