2x-y=18 x+y=8

To solve the system of equations:

1. \(2x - y = 18\) (Equation 1)
2. \(x + y = 8\) (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:

\[ \left( \frac{26}{3}, -\frac{2}{3} \right) \]