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

Question

2
𝑥
+
7
𝑦
=
14
to the equivalent equation 4x+14y=28
4
𝑥
+
14
𝑦
=
28
.(1 point)
The equation 2x+7y=14
2
𝑥
+
7
𝑦
=
14
should be multiplied by blank to produce the equivalent equation 4x+14y=28
4
𝑥
+
14
𝑦
=
28
.

Answer 1

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

So, the equation \( 2x + 7y = 14 \) multiplied by 2 gives:

\[ 2(2x) + 2(7y) = 2(14) \]

which simplifies to:

\[ 4x + 14y = 28 \]

Thus, you should multiply by 2.