Solve the system by substitution.
y, equals, 7, x, minus, 20
y=
7x−20
y, equals, 2, x
y=
2x

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.

Solve the system by substitution.
y = 7x - 20
y = 2x

Master solving systems of linear equations using substitution. This step-by-step guide tackles the system y = 7x - 20 and y = 2x, providing essential algebraic concepts and a clear solution suitable for students in Grades 8-10.

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