Question

If r = 5 z then 15 z = 3 y, then r =

• A. y
• B. 2y
• C. 4y
• D. 10y
• E. 15y

Hint:

When you have multiple equations, look for a common variable or expression. Manipulating one equation to match a part of another equation is a key strategy for substitution.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem involves solving a system of two simple equations by using substitution to find the relationship between r and y.
Step 2: Key Formula or Approach:
The goal is to express 'r' in terms of 'y'. We can do this by finding a common link between the two equations, which is the variable 'z' or an expression involving 'z'.
Step 3: Detailed Explanation:
We are given two equations:
1) \( r = 5z \)
2) \( 15z = 3y \)
Let's look at the second equation and see if we can simplify it to relate to the first equation. We can simplify \( 15z = 3y \) by dividing both sides by 3: \[ \frac{15z}{3} = \frac{3y}{3} \] \[ 5z = y \] Now we have a new expression: \( y = 5z \).
From the first equation, we know that \( r = 5z \).
Since both 'r' and 'y' are equal to the same expression (5z), they must be equal to each other.
Therefore, \( r = y \).
Step 4: Final Answer:
The value of r is equal to y. The correct option is (A).