We are solving the following system of linear equations:

1. $-20x + 6y = -6$
2. $-10x - 4 = 4$

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Step 1: Simplify the second equation

Rewriting $-10x - 4 = 4$: $-10x = 8 \quad \Rightarrow \quad x = -\frac{4}{5}.$

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Step 2: Substitute $x = -\frac{4}{5}$ into the first equation

Substituting into $-20x + 6y = -6$: $-20\left(-\frac{4}{5}\right) + 6y = -6.$ Simplify: $16 + 6y = -6.$ $6y = -22 \quad \Rightarrow \quad y = -\frac{11}{3}.$

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Final Solution:

$x = -\frac{4}{5}, \quad y = -\frac{11}{3}.$

Would you like a detailed breakdown of any step?

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Related Questions:

1. How can we solve linear systems using substitution for more complex examples?
2. What is the graphical interpretation of solving a system of linear equations?
3. Could we use elimination instead of substitution for this problem?
4. How do we check the solution for consistency?
5. What are some applications of solving linear systems in real life?

Tip: Always check your solution by substituting both values back into the original equations to verify their correctness.