Let's solve the system of equations using substitution:

We have:

1. $2x + y = 20$
2. $6x - 5y = 12$

Step 1: Solve one of the equations for one variable

From the first equation $2x + y = 20$, we can solve for $y$:

$y = 20 - 2x$

Step 2: Substitute the expression for $y$ into the second equation

Now, substitute $y = 20 - 2x$ into the second equation $6x - 5y = 12$:

$6x - 5(20 - 2x) = 12$

Step 3: Simplify and solve for $x$

Distribute the $-5$:

$6x - 100 + 10x = 12$

Combine like terms:

$16x - 100 = 12$

Add 100 to both sides:

$16x = 112$

Now, solve for $x$:

$x = \frac{112}{16} = 7$

Step 4: Substitute $x = 7$ back into the first equation to solve for $y$

Now substitute $x = 7$ into $y = 20 - 2x$:

$y = 20 - 2(7) = 20 - 14 = 6$

Final Answer:

The solution to the system of equations is $x = 7$ and $y = 6$.

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Would you like me to explain any step in more detail or assist with other questions? Here are some related questions:

1. How do you solve systems of equations using elimination?
2. Can substitution work if there are three variables instead of two?
3. How do you check if your solution is correct?
4. What happens if a system of equations has no solution?
5. How would you solve this system of equations using matrices?

Tip: Always start substitution with the simplest equation, where one variable is easily isolated.