Deriving Algebraic Relationship from Given Equations
Given Equations
We are provided with two linear equations:
- Equation 1: $P + Q = 2R$
- Equation 2: $R + S = 2P$
Expressing Variables
Rearrange the equations to express $Q$ and $S$ in terms of $P$ and $R$:
- From Equation 1: $Q = 2R - P$
- From Equation 2: $S = 2P - R$
Testing the Relationship
Let's check if the relationship $P + R = Q + S$ holds true using the expressions for $Q$ and $S$.
- Start with the right side of the potential relationship: $Q + S$.
- Substitute the expressions for $Q$ and $S$: $Q + S = (2R - P) + (2P - R)$.
- Combine like terms: $Q + S = (2R - R) + (2P - P)$.
- Simplify: $Q + S = R + P$.
- Therefore, $P + R = Q + S$.
Conclusion
The derived relationship $P + R = Q + S$ matches Option 1. This confirms that the algebraic manipulation leads directly to the correct answer.
Similar Questions
- Find the solution to the system: $y = 3x - 4$ and $y = -x + 2$.
The sum of two numbers is 40 and their difference is 4. What is the product of the numbers?
If 3x - ky + 8 = 0 and 9x - 18y + 20 = 0 have no solution, find k.
If \(3x-ky+8 = 0\) and \(9x-18y+20 = 0\) have no solution, find k.
Important Questions from Linear Equation in 2 or more Variables
Six years ago, the ratio of ages of A to B was 7 ∶ 5. After 4 years from now, the ratio of their ages will be 11 ∶ 9. What is A’s age at present?
7p - [3q - {8p - (4q - 10p)}] = ?
Surya is 25 years older than his son. In 5 years, he will be twice as old as his son. What will be Surya’s age after 3 years?
The difference between the ages of two sisters is 2 years when father’s age is 52. Father is elder by 2 years to mother. Elder sister’s age is half of mother’s age. Find the age of younger sister?
The sum of the digits of a 2 digit number is 9, When 27 is added to the number, the digits get interchanged. Find the number.
A. 45
B. 36
C. 18
D. 27
