Question

Cruz wrote a system of equations with an infinite number of solutions. One of his equations is 6x+3y=9
. What could be his second equation? (Write the equation in slope-intercept form.)(1 point)
The second equation could be y=
.
Remaining Attempts : 3
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Answer 1

To find a second equation that has an infinite number of solutions with the equation \( 6x + 3y = 9 \), we need to create an equation that is equivalent to the first.

First, let's rewrite the first equation in slope-intercept form (y = mx + b):

1. Start with the equation:
\[
6x + 3y = 9
\]

2. Subtract \( 6x \) from both sides:
\[
3y = -6x + 9
\]

3. Divide each term by 3:
\[
y = -2x + 3
\]

Now, since the second equation must be equivalent to the first, it can be any multiple of this equation. For instance, multiply the entire equation by a constant (let's say 2):

\[
2y = 2(-2x + 3)
\]
\[
2y = -4x + 6
\]

Now, rewrite it in slope-intercept form:

\[
y = -2x + 3
\]

OR you can write it in a different form (let's multiply the original answer by 2):

If we try with a different multiplier, like 1 (which keeps the equation the same) or any other number (such as -1/3), then:

Another equivalent form can be \( y = -2x + 3 \) or you can choose to express it in a different way as follows:

Let's take the original equation and rearrange it into a

1. Start from \( 6x + 3y = 9 \)
2. Take something like these equivalents:
\( 6x + 3y + 0 = 9 \) or

Another possible way can be changing '9' to another value justified by increasing or decrementing the left side equally reserving the slope.

So ultimately, a second equation could be

\[
y = -2x + 3
\]

You can choose whether you take:
Using the same slope and y-intercept:
You could also write it as:

So one possible answer could be:
\[
y = -2x + 3
\]

Or provide numerical change:
To ensure linear formation it stays equivalent.

If you take suitable multiplier or subtract/add value with same treatment.

In chance towards version it could appear multiple forms retaining consistency with \( y = m x + b \).

Thus overall the second equation would be:

\[
y = -2x + 3
\]

Feel free to adjust numbers but engage to infinite solutions which relies on that mathematic representation.