To solve the system of equations:
- (2x - y = 18) (Equation 1)
- (x + y = 8) (Equation 2)
We can use the substitution or elimination method. Here, I'll use the substitution method.
From Equation 2, we can express (y) in terms of (x):
[
y = 8 - x
]
Now, substitute this expression for (y) in Equation 1:
[
2x - (8 - x) = 18
]
Simplify the equation:
[
2x - 8 + x = 18
]
[
3x - 8 = 18
]
Now, add 8 to both sides:
[
3x = 26
]
Divide by 3:
[
x = \frac{26}{3}
]
Now, substitute (x = \frac{26}{3}) back into the equation for (y):
[
y = 8 - \frac{26}{3}
]
[
y = \frac{24}{3} - \frac{26}{3}
]
[
y = \frac{-2}{3}
]
So the solution to the system of equations is:
[
x = \frac{26}{3}, \quad y = -\frac{2}{3}
]
You can also express the solution as the ordered pair:
[
\left( \frac{26}{3}, -\frac{2}{3} \right)
]
