https://file.aiquickdraw.com/mathbot/file/1727889145807rm1elluv.jpg

The system of equations given in the image is:

\[
y = 7x
\]
\[
y = 2x + 20
\]

We can solve this system using the substitution method because both equations are solved for \( y \).

### Step 1: Set the two equations equal to each other.

Since both expressions equal \( y \), we can equate them:

\[
7x = 2x + 20
\]

### Step 2: Solve for \( x \).

To solve for \( x \), subtract \( 2x \) from both sides:

\[
7x - 2x = 20
\]

\[
5x = 20
\]

Now, divide both sides by 5:

\[
x = \frac{20}{5} = 4
\]

### Step 3: Substitute \( x = 4 \) back into one of the original equations.

Let’s use the first equation \( y = 7x \):

\[
y = 7(4) = 28
\]

### Final Answer:

\[
x = 4, \quad y = 28
\]

Would you like further clarification or details on any steps? Here are five related questions to deepen understanding:

1. How do you know when substitution is the best method to solve a system of equations?
2. Can you solve this system using the elimination method?
3. What happens if the system of equations has no solution or infinite solutions?
4. Can you solve a system of three equations with three variables in a similar way?
5. How would you graph these two equations to confirm the solution visually?

**Tip:** Always double-check your solution by substituting your values for \(x\) and \(y\) back into both original equations to verify they are correct.

Solve the system of equations: y = 7x and y = 2x + 20

Learn how to solve the system of equations y = 7x and y = 2x + 20 using the substitution method. Step-by-step solution, key algebraic concepts, and important formulas covered. Suitable for students in Grades 8-10.

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