Question

. How do you use multiplication in elimination to show that this system of equations has infinite solutions.

4x - 8y = -20
-8x + 16y = 40

(1 point)
Responses

Multiply the first equation by 4.
Multiply the first equation by 4.

Multiply the first equation by -2 and both equations will be the same.
Multiply the first equation by -2 and both equations will be the same.

Multiply the second equation by 2 and both equations willl be the same.
Multiply the second equation by 2 and both equations willl be the same.

Multiply the two equations together.

Answer 1

To show that the system of equations has infinite solutions using multiplication in elimination, we need to find a way to multiply one of the equations so that it becomes equivalent to the other equation.

The given system of equations is:

1. \( 4x - 8y = -20 \)
2. \( -8x + 16y = 40 \)

If we multiply the first equation by -2, we get:

\[
-2(4x - 8y) = -2(-20)
\]

This simplifies to:

\[
-8x + 16y = 40
\]

Now we see that the modified first equation:

\(-8x + 16y = 40\)

is exactly the same as the second equation:

\(-8x + 16y = 40\).

Since both equations are identical after this manipulation, this indicates that there are infinitely many solutions to the system, as they represent the same line.

So, the correct response is:

**Multiply the first equation by -2 and both equations will be the same.**