To solve the given system of equations using the elimination method, follow these steps:
1. Write down the system of equations:
[tex]\[
\begin{cases}
2x - 3y = 6 \\
2x - 3y = 8
\end{cases}
\][/tex]
2. Compare the two equations:
[tex]\[
2x - 3y = 6 \quad \text{(Equation 1)}
\][/tex]
[tex]\[
2x - 3y = 8 \quad \text{(Equation 2)}
\][/tex]
3. Subtract Equation 2 from Equation 1 to eliminate [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
[tex]\[
(2x - 3y) - (2x - 3y) = 6 - 8
\][/tex]
Simplifying this, we get:
[tex]\[
0 = -2
\][/tex]
4. Interpret the result:
The equation [tex]\(0 = -2\)[/tex] is a contradiction, meaning that it's not possible for the same [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values to satisfy both equations simultaneously. This tells us that there is no solution to the system of equations.
Therefore, the solution to the system of equations [tex]\(2x - 3y = 6\)[/tex] and [tex]\(2x - 3y = 8\)[/tex] is:
[tex]\[
\boxed{\text{No Solution}}
\][/tex]
