To solve the system of linear equations:
[tex]\[
\begin{cases}
4x - 5y = 3 \\
3x + 5y = 11
\end{cases}
\][/tex]
we will use the method of elimination or substitution.
### Step-by-Step Solution:
#### 1. Write down both equations:
[tex]\[
4x - 5y = 3 \quad \text{(Equation 1)}
\][/tex]
[tex]\[
3x + 5y = 11 \quad \text{(Equation 2)}
\][/tex]
#### 2. Add the two equations to eliminate [tex]\(y\)[/tex]:
[tex]\[
(4x - 5y) + (3x + 5y) = 3 + 11
\][/tex]
This simplifies to:
[tex]\[
(4x + 3x) + (-5y + 5y) = 14
\][/tex]
[tex]\[
7x = 14
\][/tex]
#### 3. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{14}{7} = 2
\][/tex]
#### 4. Substitute [tex]\(x = 2\)[/tex] back into one of the original equations to find [tex]\(y\)[/tex]. Let's use Equation 1:
[tex]\[
4(2) - 5y = 3
\][/tex]
[tex]\[
8 - 5y = 3
\][/tex]
Subtract 8 from both sides:
[tex]\[
-5y = 3 - 8
\][/tex]
[tex]\[
-5y = -5
\][/tex]
Divide by -5:
[tex]\[
y = 1
\][/tex]
So, the solution to the system of equations is:
[tex]\[
(x, y) = (2, 1)
\][/tex]
#### 5. Check the solution in both equations:
Substitute into Equation 1:
[tex]\[
4(2) - 5(1) = 8 - 5 = 3 \quad \text{Correct}
\][/tex]
Substitute into Equation 2:
[tex]\[
3(2) + 5(1) = 6 + 5 = 11 \quad \text{Correct}
\][/tex]
Both checks confirm that the solution is correct.
### Multiple Choice Selection:
The correct solution corresponds to the choice:
[tex]\[
a. (2, 1)
\][/tex]
Therefore, the answer is [tex]\( \boxed{1} \)[/tex].
