4y + 3x = -6

Question

y - x = -5

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

Multiply by ___ on both sides

Answer 1

To eliminate the x-terms in the system of equations, we want to manipulate the equations so that when we add or subtract them, the x-terms cancel out.

The system of equations is:

1. \( 4y + 3x = -6 \)
2. \( y - x = -5 \)

We can multiply the second equation by 3. This will give both equations the same coefficient for \( x \) (3 for the first equation and -3 for the second equation):

The first equation remains:

1. \( 4y + 3x = -6 \)

For the second equation, multiplying by 3: \[ 3(y - x) = 3(-5) \] which simplifies to: \[ 3y - 3x = -15 \]

Now we can rewrite the system:

1. \( 4y + 3x = -6 \)
2. \( 3y - 3x = -15 \)

Now, we can add the two equations together. The \( 3x \) from the first equation and the \( -3x \) from the second equation will cancel out.

So, to eliminate the x-terms, multiply the second equation by 3. Therefore, you would fill in the blank as follows:

Multiply by 3 on both sides.