Let's break down the problem from the image:

Part (a)

We are asked to complete the following equation transformation: Given $x + 3y = 7$, multiply both sides of the equation by 5 to create an equivalent equation.

So, starting with:

$x + 3y = 7$

Multiplying both sides by 5:

$5(x + 3y) = 5 \times 7$

Which simplifies to:

$5x + 15y = 35$

Thus, the equivalent equation is:

$5x + 15y = 35$

Part (b)

We are asked to find the value of $x$ if $y = 1$.

From the equation $5x + 15y = 35$, substitute $y = 1$:

$5x + 15(1) = 35$

This simplifies to:

$5x + 15 = 35$

Now, subtract 15 from both sides:

$5x = 35 - 15$

$5x = 20$

Finally, divide both sides by 5:

$x = \frac{20}{5} = 4$

So, the value of $x$ is $4$.

Would you like more details on the steps? Here are some related questions to expand your understanding:

1. How do you check if two equations are equivalent?
2. What happens to the equation if you multiply both sides by a different constant?
3. What method can be used to solve simultaneous equations?
4. How can you verify the solution $x = 4$ for $y = 1$?
5. What other transformations could be applied to the original equation $x + 3y = 7$?

Tip: When working with equations, remember that whatever you do to one side of the equation (like multiplication or division), you must do to the other side to keep it balanced.