To solve the system of equations:
- ( 2x - 9y = 11 ) (Equation 1)
- ( 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)
]
