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
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 should multiply the entire equation \( 2x + 7y = 14 \) by 2.

So, \( 2 \cdot (2x + 7y) = 2 \cdot 14 \) gives you:

\[ 4x + 14y = 28. \]

The correct answer is 2.