Let's solve the given system of equations step-by-step to eliminate one of the variables and see what the resulting equation becomes.
We are given the following system of equations:
[tex]\[
\begin{array}{l}
2x + 3y = 7 \quad \text{(Equation 1)} \\
3x - 3y = 3 \quad \text{(Equation 2)}
\end{array}
\][/tex]
Our objective is to eliminate one of the variables, which in this case is [tex]\( y \)[/tex].
First, we'll add the two equations to eliminate [tex]\( y \)[/tex]:
[tex]\[
(2x + 3y) + (3x - 3y) = 7 + 3
\][/tex]
Simplifying the left-hand side:
[tex]\[
2x + 3x + 3y - 3y = 7 + 3
\][/tex]
Combine like terms:
[tex]\[
(2x + 3x) + (3y - 3y) = 7 + 3
\][/tex]
Since [tex]\( 3y - 3y = 0 \)[/tex], the equation simplifies to:
[tex]\[
5x + 0 = 10
\][/tex]
So we end up with the following equation:
[tex]\[
5x = 10
\][/tex]
It is clear that the correct form of the equation when one variable is eliminated is:
[tex]\[
5x = 10
\][/tex]
Therefore, the correct answer is:
B. [tex]\( 5x = 10 \)[/tex]
