The problem involves solving the following system of linear equations:

$-3x + 6y = 9$ $5x + 7y = -49$

Step 1: Simplify the first equation (if needed)

Divide the first equation by $-3$ to make calculations simpler:

$x - 2y = -3 \quad \text{(Equation 1')}$

Step 2: Solve for $x$ from Equation 1'

From $x - 2y = -3$, solve for $x$:

$x = 2y - 3$

Step 3: Substitute $x = 2y - 3$ into the second equation

Substitute $x = 2y - 3$ into $5x + 7y = -49$:

$5(2y - 3) + 7y = -49$

Simplify: $10y - 15 + 7y = -49$ $17y - 15 = -49$ $17y = -34$ $y = -2$

Step 4: Solve for $x$

Substitute $y = -2$ into $x = 2y - 3$:

$x = 2(-2) - 3$ $x = -4 - 3$ $x = -7$

Final Answer:

The solution is $(-7, -2)$, which corresponds to option A.

Would you like a detailed explanation of any step? Here are some related questions you might explore:

1. How can substitution help in solving a system of linear equations?
2. What is the advantage of simplifying one equation before solving?
3. Can elimination also solve this system of equations?
4. What are the steps to graphically solve a system of linear equations?
5. How does changing coefficients affect the solution of a system of equations?

Tip: Always verify the solution by substituting the values back into the original equations!