To find the value of \(4x + 3y\) given the equations:

1. \(3x + 2y = 5\)
2. \(5x + 4y = 9\)

we can solve this system of linear equations. Here’s the step-by-step method:

Step 1: Solve the System of Equations

Equation 1:
\[
3x + 2y = 5
\]

Equation 2:
\[
5x + 4y = 9
\]

To eliminate one of the variables, we can multiply Equation 1 by 2 to align the coefficients of \(y\):

\[
2 \times (3x + 2y) = 2 \times 5
\]
\[
6x + 4y = 10
\]

Now subtract Equation 2 from this result:

\[
(6x + 4y) - (5x + 4y) = 10 - 9
\]
\[
x = 1
\]

Step 2: Substitute \(x = 1\) into Equation 1 to find \(y\):

Substitute \(x = 1\) into Equation 1:

\[
3(1) + 2y = 5
\]
\[
3 + 2y = 5
\]
\[
2y = 2
\]
\[
y = 1
\]

Step 3: Calculate \(4x + 3y\) using \(x = 1\) and \(y = 1\):

\[
4x + 3y = 4(1) + 3(1) = 4 + 3 = 7
\]

The value of \(4x + 3y\) is 7

The correct answer is E. 7