Question

Question

Which of the following shows a system of equations equivalent to 2x+7y=14
and 4x+5y=10
?(1 point)
Responses

2x+7y=14
and 2x+5y=5
2 x plus 7 y equals 14 and 2 x plus 5 y equals 5

4x+14y=28
and 8x+10y=10
4 x plus 14 y equals 28 and 8 x plus 10 y equals 10

4x+14y=14
and 4x+5y=10
4 x plus 14 y equals 14 and 4 x plus 5 y equals 10

2x+7y=14
and 8x+10y=20

Answer 1

To find a system of equations equivalent to:

1. \(2x + 7y = 14\)
2. \(4x + 5y = 10\)

we need to manipulate these equations by multiplication or division to maintain their equivalence.

Starting with the first equation, if we multiply it by 2, we get:

\[ 2(2x + 7y) = 2(14) \implies 4x + 14y = 28 \]

For the second equation, if we multiply it by 2, we get:

\[ 2(4x + 5y) = 2(10) \implies 8x + 10y = 20 \]

Therefore, the equivalent system is:

\[ 4x + 14y = 28 \quad \text{and} \quad 8x + 10y = 20 \]

The correct response from the options is:

4x + 14y = 28 and 8x + 10y = 20.