We are given the system of equations:

1. $y = 2x$
2. $y = 3x - 10$

To solve this system, we can use the method of substitution. Since both equations equal $y$, we can set them equal to each other:

$2x = 3x - 10$

Now, solve for $x$:

1. Subtract $2x$ from both sides: $0 = x - 10$

2. Add 10 to both sides: $x = 10$

Now that we have $x = 10$, substitute this value into either of the original equations to find $y$. Let's use the first equation $y = 2x$:

$y = 2(10) = 20$

Thus, the solution to the system of equations is the ordered pair $(10, 20)$.

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Would you like a more detailed explanation or have any questions about this solution? Here are some related questions:

1. What would the solution be if the two equations were $y = 2x$ and $y = 4x - 6$?
2. How do you graph these two equations on a coordinate plane?
3. What happens if the system of equations is inconsistent, like when the lines are parallel?
4. Can you solve a system with more than two variables using substitution?
5. How do you check your solution for accuracy in this system?

Tip: Always check the solution by substituting the values back into the original equations to confirm that they are true!