The system of equations given is:

$-6x + 4y = 26$ $5x + 2y = 37$

You are asked how the system can be altered so that adding the equations eliminates one of the variables.

Step 1: Analyze the coefficients

• In elimination, we want to make the coefficients of either $x$ or $y$ opposites in both equations so that they cancel out when added.

Coefficients of $x$:

• The coefficients are $-6$ and $5$. To eliminate $x$, we would need to make the coefficients multiples of each other.

Coefficients of $y$:

• The coefficients are $4$ and $2$. To eliminate $y$, it is easier to multiply the second equation by $-2$ to make the coefficients of $y$ opposites.

Step 2: Apply the best modification

• If we multiply the second equation by $-2$, the second equation becomes: $-10x - 4y = -74$

Now the system becomes: $-6x + 4y = 26$ $-10x - 4y = -74$ When added, the $y$ terms will cancel out.

Answer:

The correct option is D. Multiply the second equation by $-2$.

Would you like a more detailed breakdown of any steps, or do you have any other questions?

Here are 5 related questions to further your understanding:

1. How do you know when elimination is the best method to solve a system of equations?
2. Can elimination always be used if the coefficients are not easily manipulated?
3. What happens if you multiply both equations by constants but do not cancel a variable?
4. How can you use substitution in this case, and which method would be faster?
5. What if the system of equations had fractions—how would you handle them in elimination?

Tip: Always check if multiplying by a negative constant will make elimination simpler by creating opposite coefficients.