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=
.

Answer 1

To have a system of equations with an infinite number of solutions, the second equation must represent the same line as the first equation. The equation given is:

\[ 6x + 3y = 9 \]

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

1. Solve for \(y\):
\[
3y = -6x + 9
\]

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

Now, to create a second equation that has the same slope and y-intercept (and hence is equivalent), we can multiply this by any non-zero constant. For example, if we multiply the entire equation by 2, we get:

\[
2y = -4x + 6
\]

Rearranging this into standard form results in:

\[
4x + 2y = 6
\]

However, we are asked for the slope-intercept form, so we will keep it as:

\[
y = -2x + 3
\]

Thus, one possible second equation that Cruz could write is:

\[
y = -2x + 3
\]

This means the second equation could be:

\[
y = -2x + 3
\]