Answer :
To solve [tex]\(2x - y = 7\)[/tex] and [tex]\(y = 2x + 3\)[/tex], we can proceed step by step.
1. Substitute [tex]\(y\)[/tex] from the second equation into the first equation:
[tex]\[ 2x - (2x + 3) = 7 \][/tex]
Simplify this expression:
[tex]\[ 2x - 2x - 3 = 7 \][/tex]
Combine like terms:
[tex]\[ -3 = 7 \][/tex]
2. The simplified equation [tex]\(-3 = 7\)[/tex] is a contradiction, meaning that it is not true for any values of [tex]\(x\)[/tex].
Since substituting [tex]\(y = 2x + 3\)[/tex] into [tex]\(2x - y = 7\)[/tex] results in a contradiction, we can conclude that there is no solution to the system of equations.
Therefore, the correct answer is:
[tex]\[ \boxed{\text{no solution}} \][/tex]
1. Substitute [tex]\(y\)[/tex] from the second equation into the first equation:
[tex]\[ 2x - (2x + 3) = 7 \][/tex]
Simplify this expression:
[tex]\[ 2x - 2x - 3 = 7 \][/tex]
Combine like terms:
[tex]\[ -3 = 7 \][/tex]
2. The simplified equation [tex]\(-3 = 7\)[/tex] is a contradiction, meaning that it is not true for any values of [tex]\(x\)[/tex].
Since substituting [tex]\(y = 2x + 3\)[/tex] into [tex]\(2x - y = 7\)[/tex] results in a contradiction, we can conclude that there is no solution to the system of equations.
Therefore, the correct answer is:
[tex]\[ \boxed{\text{no solution}} \][/tex]
