Explanation of Solution to the Given Equations:
- Given Equations:
X ÷ p = y ÷ q = 2
x + y = p + q
- Key Points:
1. The first equation can be rewritten as X = 2p and y = 2q.
2. Substituting these values in the second equation gives 2p + 2q = p + q.
3. Simplifying the equation leads to p = q.
4. Therefore, the solutions that satisfy the given equations are X = 2p, y = 2q, and p = q.
- Explanation:
The first equation states that the ratio of X to p is equal to the ratio of y to q, both equal to 2. This implies that X is twice p and y is twice q. Substituting these values into the second equation results in 2p + 2q = p + q. By simplifying this equation, we find that p = q. Consequently, the solutions that satisfy the given equations are X = 2p, y = 2q, and p = q. This relationship ensures that the equations are balanced and consistent with each other.