To solve the given system of equations, we can use substitution or elimination. We will use substitution in this case.
Given equations are:
1. [tex]\( 2x - y = 7 \)[/tex]
2. [tex]\( y = 2x + 3 \)[/tex]
### Step-by-Step Solution:
1. First, we will substitute the value of [tex]\( y \)[/tex] from the second equation [tex]\( y = 2x + 3 \)[/tex] into the first equation [tex]\( 2x - y = 7 \)[/tex].
[tex]\[
2x - (2x + 3) = 7
\][/tex]
2. Now, simplify the equation:
[tex]\[
2x - 2x - 3 = 7
\][/tex]
3. This simplifies further to:
[tex]\[
-3 = 7
\][/tex]
4. Since [tex]\(-3 = 7\)[/tex] is a contradiction (it is not true), there is no value of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that can satisfy both equations simultaneously.
### Conclusion:
Given the contradiction we reached, there is no solution to this system of equations.
Therefore, the correct answer is:
no solution