Question

What operation needs to be performed to go from the equation 2x+7y=14
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 need to multiply the entire equation by 2.

So, you would multiply \( 2x + 7y = 14 \) by 2:

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

This results in:

\[
4x + 14y = 28
\]

Therefore, the equation \( 2x + 7y = 14 \) should be multiplied by \( 2 \).