https://file.aiquickdraw.com/mathbot/file/1728893064502lc8p4eju.jpg

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.

Copy and complete the working below to create an equation that is equivalent to x + 3y = 7. If y = 1, what is the value of x that satisfies these equations?

Learn how to transform and solve the linear equation x + 3y = 7, including creating an equivalent equation by multiplication and finding the value of x when y = 1. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation