Question

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

Answer 1

To determine a system of equations equivalent to

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

we can manipulate these equations using various methods such as multiplication or addition/subtraction.

### Step 1: Rewrite the equations

We can multiply the first equation by 2 to get:

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

Now we have:

1. \( 4x + 14y = 28 \)
2. \( 4x + 5y = 10 \)

### Step 2: Create a new system of equations

The new system of equations now looks like:

1. \( 4x + 14y = 28 \)
2. \( 4x + 5y = 10 \)

### Step 3: Check for a proportional relationship

To check whether the second equation can be manipulated to maintain equivalence with the original equations, we can explore scaling and adding/subtracting equations.

However, without specific multiple-choice options, it's essential to maintain the same set of equations while forming an equivalent system, so the valid equivalent equations could differ.

### Conclusion

To summarize, the transformed equations:

\[
4x + 14y = 28
\]
\[
4x + 5y = 10
\]

are equivalent to the original equations, but if you need specific options, please provide them for clarity.