Question

Which of the following shows a system of equations equivalent to 2x+7y=14 and 4x+5y=10 ?(1 point)%0D%0AResponses%0D%0A%0D%0A 2x+7y=14 and 2x+5y=5%0D%0A2 x plus 7 y equals 14 and 2 x plus 5 y equals 5%0D%0A%0D%0A 4x+14y=14 and 4x+5y=10%0D%0A4 x plus 14 y equals 14 and 4 x plus 5 y equals 10%0D%0A%0D%0A 2x+7y=14 and 8x+10y=20%0D%0A2 x plus 7 y equals 14 and 8 x plus 10 y equals 20%0D%0A%0D%0A 4x+14y=28 and 8x+10y=10

Answer 1

To find a system of equations that is equivalent to the given equations \(2x + 7y = 14\) and \(4x + 5y = 10\), we can manipulate these equations, such as by multiplying both sides by the same non-zero constant.

1. **First equation:** \(2x + 7y = 14\) can be multiplied by 2 to get:
\[
4x + 14y = 28
\]

2. **Second equation:** \(4x + 5y = 10\) can be multiplied by 2 to get:
\[
8x + 10y = 20
\]

Now we can check the provided options:

- **Option 1:** \(2x + 7y = 14\) and \(2x + 5y = 5\) (not equivalent)
- **Option 2:** \(4x + 14y = 14\) and \(4x + 5y = 10\) (not equivalent, wrong coefficient for first equation)
- **Option 3:** \(2x + 7y = 14\) and \(8x + 10y = 20\) (correct)
- **Option 4:** \(4x + 14y = 28\) and \(8x + 10y = 10\) (not equivalent)

The correct response is **Option 3**: \(2x + 7y = 14\) and \(8x + 10y = 20\).