We are given the system of equations:

1. $y = 7x - 20$
2. $y = 2x$

We can solve this system using substitution. Since both equations give us an expression for $y$, we can set them equal to each other:

$7x - 20 = 2x$

Now, solve for $x$:

1. Subtract $2x$ from both sides: $7x - 2x - 20 = 0$ $5x - 20 = 0$

2. Add 20 to both sides: $5x = 20$

3. Divide both sides by 5: $x = 4$

Now that we have $x = 4$, substitute this value into one of the original equations to find $y$. We'll use $y = 2x$:

$y = 2(4) = 8$

Thus, the solution to the system is $x = 4$ and $y = 8$.

Final Answer:

$x = 4, \quad y = 8$

Would you like more details or have any questions?

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Here are 5 related questions to further explore this topic:

1. What happens if you solve the system graphically?
2. How would you solve a similar system with a non-linear equation?
3. Can you solve a system of equations with more than two variables by substitution?
4. What are the advantages of using substitution over other methods like elimination?
5. How do you solve a system of equations if no solution exists?

Tip: Always check your solution by substituting the values of $x$ and $y$ back into both original equations to ensure they hold true.