2х-9у=11 7х+9у=25

To solve the system of equations:

1. \( 2x - 9y = 11 \) (Equation 1)
2. \( 7x + 9y = 25 \) (Equation 2)

We can use the elimination or substitution method. Here, we will use the elimination method.

First, let's add both equations together, aiming to eliminate \( y \):

From Equation 1: \[ 2x - 9y = 11 \]

From Equation 2: \[ 7x + 9y = 25 \]

Add Equation 1 and Equation 2: \[ (2x - 9y) + (7x + 9y) = 11 + 25 \] This simplifies to: \[ 2x + 7x - 9y + 9y = 36 \] \[ 9x = 36 \] Now, solve for \( x \): \[ x = \frac{36}{9} \] \[ x = 4 \]

Next, substitute \( x = 4 \) back into one of the original equations to find \( y \). We'll use Equation 1: \[ 2(4) - 9y = 11 \] \[ 8 - 9y = 11 \] Now, isolate \( y \): \[ -9y = 11 - 8 \] \[ -9y = 3 \] \[ y = \frac{3}{-9} \] \[ y = -\frac{1}{3} \]

So the solution to the system of equations is: \[ x = 4, \quad y = -\frac{1}{3} \]

Thus, the final answer is: \[ (x, y) = \left( 4, -\frac{1}{3} \right) \]