Question

The solution of system of equations \( \frac{x}{2025} + \frac{y}{2026} = 2 \) and \( \frac{2x}{2025} - \frac{y}{2026} = 1 \) is:

• A. \( x = 4025, \, y = 2026 \)
• B. \( x = 4040, \, y = 2025 \)
• C. \( x = 2025, \, y = 2026 \)
• D. \( x = 4030, \, y = 2027 \)

Hint:

For solving systems of linear equations, it’s effective to multiply each equation by a common factor to eliminate denominators. Then solve for one variable and substitute it into the other equation.

Answer 1

The Correct Option is C

Solve the system of equations. We are given the system: \[ \frac{x}{2025} + \frac{y}{2026} = 2 \quad \text{(1)} \] \[ \frac{2x}{2025} - \frac{y}{2026} = 1 \quad \text{(2)} \] First, solve for one variable from equation (1): \[ \frac{x}{2025} = 2 - \frac{y}{2026} \quad \Rightarrow \quad x = 2025 \left( 2 - \frac{y}{2026} \right) \] Substitute this expression for \( x \) into equation (2), and solve for \( y \). After solving, you find \( y = 2026 \) and substituting back \( y \) into the equation gives \( x = 2025 \).