To solve the system of equations using substitution, we start with the two equations given:
- \( -10x + 3y = 34 \)
- \( y = -8x \)
Since the second equation is already solved for \( y \), we can substitute this expression into the first equation.
Substituting \( y = -8x \) into \( -10x + 3y = 34 \):
\[ -10x + 3(-8x) = 34 \]
Now, simplify the equation:
\[ -10x - 24x = 34 \]
Combine the terms:
\[ -34x = 34 \]
Next, solve for \( x \):
\[ x = \frac{34}{-34} = -1 \]
Now that we have \( x \), we can find \( y \) using the expression for \( y \) in the second equation:
\[ y = -8x \]
Substitute \( x = -1 \):
\[ y = -8(-1) = 8 \]
Therefore, the solution to the system of equations is:
\[ (x, y) = (-1, 8) \]
To summarize, the final answer is:
\[ \boxed{(-1, 8)} \]
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