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):
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Solve for \(y\): \[ 3y = -6x + 9 \]
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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:
\[ y = -2x + 3 \]
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