To determine a system of equations equivalent to
- \( 2x + 7y = 14 \)
- \( 4x + 5y = 10 \),
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:
- \( 4x + 14y = 28 \)
- \( 4x + 5y = 10 \)
Step 2: Create a new system of equations
The new system of equations now looks like:
- \( 4x + 14y = 28 \)
- \( 4x + 5y = 10 \)
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.