To solve this system of equations, let's go through the steps:

The system of equations given is:

1. $y = 3x$
2. $2x + 2y = 34$

Step 1: Substitute $y$ in the second equation

Since $y = 3x$ from the first equation, substitute $y$ in the second equation: $2x + 2(3x) = 34$

Step 2: Simplify and Solve for $x$

Expanding the terms: $2x + 6x = 34$ Combine like terms: $8x = 34$ Now, divide both sides by 8 to solve for $x$: $x = \frac{34}{8} = \frac{17}{4} = 4.25$

Step 3: Substitute $x$ back to find $y$

Now that we have $x = 4.25$, substitute it back into the equation $y = 3x$: $y = 3 \times 4.25 = 12.75$

Solution

The solution to the system is: $x = 4.25, \quad y = 12.75$

Would you like more details, or do you have any questions?

Here are 5 related questions for further practice:

1. How would you solve if the first equation was $y = 2x$ instead of $y = 3x$?
2. What if the second equation was $2x + y = 34$?
3. How can you check if the solution is correct by substituting back?
4. What happens if both equations are in terms of $y$ and you need to solve for $x$?
5. How would you graph these equations to find the intersection point visually?

Tip: Always verify your solution by substituting it back into the original equations to ensure both are satisfied.