4x - 8y = 20

Question

3x + 4y = 5

How can you eliminate the y-terms in this system?

multiply by ___ on both sides

Answer 1

To eliminate the \( y \)-terms in the system of equations, you'll want to make the coefficients of \( y \) equal in both equations.

Here are the equations you have:

1. \( 4x - 8y = 20 \)
2. \( 3x + 4y = 5 \)

To eliminate \( y \), you can multiply the first equation by \( 1 \) (which doesn't change it) and the second equation by \( 2 \) (so the coefficients of \( y \) will be the same in magnitude).

1. \( 4x - 8y = 20 \) (multiply by \( 1 \))
2. \( 3x + 4y = 5 \) (multiply by \( 2 \))

After multiplying the second equation by \( 2 \), we get:

\[ 2(3x + 4y) = 2(5) \] \[ 6x + 8y = 10 \]

Now you have the system:

1. \( 4x - 8y = 20 \)
2. \( 6x + 8y = 10 \)

Now you can add both equations together to eliminate \( y \):

\[ (4x - 8y) + (6x + 8y) = 20 + 10 \] \[ 10x = 30 \]

So, to eliminate the \( y \)-terms, multiply the second equation by \( 2 \).