2. $$ \begin{aligned}-4 x+3 y & =0 \ 4 x+9 y & =36\end{aligned} $$

Question

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{aligned}
-4x + 3y &= 0 \quad \text{(1)} \
4x + 9y &= 36 \quad \text{(2)}
\end{aligned}
$$

we can use the substitution method.

### Step 1: Solve Equation (1) for $$ x $$

From equation (1):

$$
-4x + 3y = 0
$$

Rearrange to solve for $$ x $$:

$$
-4x = -3y \
x = \frac{3}{4}y
$$

### Step 2: Substitute $$ x $$ into Equation (2)

Substitute $$ x = \frac{3}{4}y $$ into equation (2):

$$
4\left(\frac{3}{4}y\right) + 9y = 36
$$

Simplify:

$$
3y + 9y = 36 \
12y = 36 \
y = \frac{36}{12} \
y = 3
$$

### Step 3: Find $$ x $$ Using the Value of $$ y $$

Substitute $$ y = 3 $$ back into $$ x = \frac{3}{4}y $$:

$$
x = \frac{3}{4} \times 3 \
x = \frac{9}{4} \
x = 2.25
$$

### **Solution**

The system has the solution:

$$
x = \frac{9}{4} \quad \text{and} \quad y = 3
$$

Expressed as an ordered pair:

$$
\left( \frac{9}{4},\ 3 \right)
$$
The solution is $$ x = \frac{9}{4} $$ and $$ y = 3 $$.

2. \( \begin{aligned}-4 x+3 y & =0 \\ 4 x+9 y & =36\end{aligned} \)