Question

Fill in the blanks so that the following system of linear equations has infinite solutions.
y= -8x+8

Answer 1

To ensure that the system of linear equations has infinite solutions, the second equation must be a multiple of the first equation. The first equation you provided is:

\[
y = -8x + 8
\]

To create a second equation that has infinite solutions with the first one, we can multiply both sides of the first equation by any non-zero constant \( k \).

Let's choose \( k = 2 \) as an example:

\[
2y = 2(-8x + 8)
\]
\[
2y = -16x + 16
\]

Now, if we rewrite this, we have:

\[
y = -8x + 8
\]

So our second equation, which has infinite solutions with the first, can be:

\[
2y = -16x + 16
\]

Thus, our system of linear equations is:

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

Both equations describe the same line and therefore have infinite solutions. You can choose any non-zero constant \( k \) to generate a valid second equation.