To solve the system of equations:
- \( 2x + 3y = 4 \) (Equation 1)
- \( 5x + y = 10 \) (Equation 2)
We can use substitution or elimination. Here, we will use substitution.
First, let's solve Equation 2 for \( y \):
\[ y = 10 - 5x \]
Now, we can substitute this expression for \( y \) into Equation 1:
\[ 2x + 3(10 - 5x) = 4 \]
Now, distribute the \( 3 \):
\[ 2x + 30 - 15x = 4 \]
Combine like terms:
\[ -13x + 30 = 4 \]
Now, isolate \( x \):
\[ -13x = 4 - 30 \] \[ -13x = -26 \]
Now, divide both sides by -13:
\[ x = 2 \]
Thus, the x-value of the solution for this system is \( \boxed{2} \).