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Complete the statement with an equation that makes the statement true.(1 point)

The system of equations 3x+4y=1 and y= ___
has an infinite number of solutions.

1 answer

For the system of equations to have an infinite number of solutions, the second equation must be equivalent to the first equation.

The equation given is \(3x + 4y = 1\). To express \(y\) in terms of \(x\), we can rearrange the equation:

  1. Subtract \(3x\) from both sides: \[ 4y = 1 - 3x \]
  2. Divide both sides by \(4\): \[ y = \frac{1 - 3x}{4} \]

Thus, the complete statement is:

The system of equations \(3x + 4y = 1\) and \(y = \frac{1 - 3x}{4}\) has an infinite number of solutions.