Let's solve the system of equations using substitution.

Given system: $10x + 6y = 20$ $-3x - y = -14$

Step 1: Solve for $y$ in terms of $x$

We take the second equation: $-3x - y = -14$ Solve for $y$: $y = -3x + 14$

Step 2: Substitute $y = -3x + 14$ into the first equation

$10x + 6(-3x + 14) = 20$ Distribute the 6: $10x - 18x + 84 = 20$ $-8x + 84 = 20$ Subtract 84 from both sides: $-8x = -64$ Divide by -8: $x = 8$

Step 3: Solve for $y$

Substituting $x = 8$ into $y = -3x + 14$: $y = -3(8) + 14$ $y = -24 + 14$ $y = -10$

Final Answer:

$(x, y) = (8, -10)$

Would you like a detailed breakdown of any step?

Here are some related questions to explore:

1. How do you solve a system of equations using the elimination method?
2. What are the advantages of the substitution method over other methods?
3. How can you check if a solution to a system of equations is correct?
4. Can a system of equations have no solution or infinitely many solutions?
5. How can you graphically represent the solution to a system of equations?

Tip: Always substitute your solution back into the original equations to verify correctness!