What operation needs to be performed to go from the equation 2x+7y=14%0D%0A2%0D%0A𝑥%0D%0A+%0D%0A7%0D%0A𝑦%0D%0A=%0D%0A14%0D%0A to the equivalent equation 4x+14y=28%0D%0A4%0D%0A𝑥%0D%0A+%0D%0A14%0D%0A𝑦%0D%0A=%0D%0A28%0D%0A .(1 point)%0D%0AThe equation 2x+7y=14%0D%0A2%0D%0A𝑥%0D%0A+%0D%0A7%0D%0A𝑦%0D%0A=%0D%0A14%0D%0A should be multiplied by to produce the equivalent equation 4x+14y=28%0D%0A4%0D%0A𝑥%0D%0A+%0D%0A14%0D%0A𝑦%0D%0A=%0D%0A28%0D%0A.

Question

What operation needs to be performed to go from the equation  2x+7y=14%0D%0A2%0D%0A𝑥%0D%0A+%0D%0A7%0D%0A𝑦%0D%0A=%0D%0A14%0D%0A  to the equivalent equation  4x+14y=28%0D%0A4%0D%0A𝑥%0D%0A+%0D%0A14%0D%0A𝑦%0D%0A=%0D%0A28%0D%0A .(1 point)%0D%0AThe equation 2x+7y=14%0D%0A2%0D%0A𝑥%0D%0A+%0D%0A7%0D%0A𝑦%0D%0A=%0D%0A14%0D%0A should be multiplied by  to produce the equivalent equation 4x+14y=28%0D%0A4%0D%0A𝑥%0D%0A+%0D%0A14%0D%0A𝑦%0D%0A=%0D%0A28%0D%0A.

GPT-4o mini · Answer

To transform the equation $ 2x + 7y = 14 $ into the equation $ 4x + 14y = 28 $, you can multiply the entire equation by 2. Here’s the calculation: 1. Start with the original equation: $$ 2x + 7y = 14 $$ 2. Multiply each term by 2: $$ 2(2x) + 2(7y) = 2(14) $$ 3. This simplifies to: $$ 4x + 14y = 28 $$ Thus, the operation that needs to be performed is to multiply the equation $ 2x + 7y = 14 $ by **2**.