Select the correct answer.

Solve the system of equations below:
[tex]\[
\begin{array}{l}
5x + 2y = 9 \\
2x - 3y = 15
\end{array}
\][/tex]

A. [tex]\((-3, 3)\)[/tex]
B. [tex]\((-3, 12)\)[/tex]
C. [tex]\((12, -3)\)[/tex]
D. [tex]\((3, -3)\)[/tex]



Answer :

Let's solve the system of equations step-by-step to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].

The given system of equations is:

[tex]\[ \begin{array}{l} 5x + 2y = 9 \\ 2x - 3y = 15 \end{array} \][/tex]

### Step 1: Solve one of the equations for one variable

First, we can solve the first equation for [tex]\( y \)[/tex]:

[tex]\[ 5x + 2y = 9 \quad \Rightarrow \quad 2y = 9 - 5x \quad \Rightarrow \quad y = \frac{9 - 5x}{2} \][/tex]

### Step 2: Substitute the expression for [tex]\( y \)[/tex] into the second equation

Now, substitute [tex]\( y = \frac{9 - 5x}{2} \)[/tex] into the second equation:

[tex]\[ 2x - 3 \left( \frac{9 - 5x}{2} \right) = 15 \][/tex]

### Step 3: Simplify the equation

Distribute the [tex]\(-3\)[/tex]:

[tex]\[ 2x - \frac{27 - 15x}{2} = 15 \][/tex]

Multiply through by 2 to clear the fraction:

[tex]\[ 4x - (27 - 15x) = 30 \][/tex]

Simplify inside the parentheses:

[tex]\[ 4x - 27 + 15x = 30 \][/tex]

Combine like terms:

[tex]\[ 19x - 27 = 30 \][/tex]

### Step 4: Solve for [tex]\( x \)[/tex]

Add 27 to both sides:

[tex]\[ 19x = 57 \][/tex]

Divide by 19:

[tex]\[ x = 3 \][/tex]

### Step 5: Solve for [tex]\( y \)[/tex]

Now, substitute [tex]\( x = 3 \)[/tex] back into the expression we found for [tex]\( y \)[/tex]:

[tex]\[ y = \frac{9 - 5(3)}{2} = \frac{9 - 15}{2} = \frac{-6}{2} = -3 \][/tex]

### Result

So, the solution to the system of equations is:

[tex]\[ x = 3 \quad \text{and} \quad y = -3 \][/tex]

Thus, the correct answer is

[tex]\[ \boxed{(3, -3)} \][/tex]

So, the answer is:
D. [tex]\((3, -3)\)[/tex]