To ensure that the system of equations \(3x + 4y = 1\) and \(y =\) has an infinite number of solutions, the second equation must be equivalent to the first one.
To express \(y\) in terms of \(x\) from the first equation, we can rearrange it:
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Start with the equation: \[ 3x + 4y = 1 \]
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Isolate \(y\): \[ 4y = 1 - 3x \] \[ y = \frac{1 - 3x}{4} \] \[ y = \frac{1}{4} - \frac{3}{4}x \]
Therefore, the complete statement would be:
The system of equations \(3x + 4y = 1\) and \(y = \frac{1}{4} - \frac{3}{4}x\) has an infinite number of solutions.