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.
Answers
GPT-4o mini
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**.
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**.