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What operation needs to be performed to go from the equation 2x + 7y = 14 to the equivalent equation 4x + 14y = 28.

The equation 2x + 7y = 14 should be multiplied by__ to produce the equivalent equation 4x + 14y = 28.

1 answer

To go from the equation \(2x + 7y = 14\) to the equivalent equation \(4x + 14y = 28\), we can multiply the entire equation by 2.

Here’s the breakdown:

  1. Start with the original equation: \[ 2x + 7y = 14 \]

  2. Multiply each term by 2: \[ 2(2x) + 2(7y) = 2(14) \] This simplifies to: \[ 4x + 14y = 28 \]

Thus, the operation that needs to be performed is to multiply the original equation by 2.