7) In the equation $$ 2 x-3 y=12 $$, solve for $$ y $$ when $$ x=0 $$ and solve for $$ x $$ when $$ y=0 $$.

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To solve the equation $$ 2x - 3y = 12 $$ for different variables, we'll perform the following steps:

### 1. Solve for $$ y $$ when $$ x = 0 $$

**Step 1:** Substitute $$ x = 0 $$ into the equation.

$$
2(0) - 3y = 12
$$

**Step 2:** Simplify the equation.

$$
0 - 3y = 12 \
-3y = 12
$$

**Step 3:** Solve for $$ y $$.

$$
y = \frac{12}{-3} \
y = -4
$$

**Solution:** When $$ x = 0 $$, $$ y = -4 $$.

### 2. Solve for $$ x $$ when $$ y = 0 $$

**Step 1:** Substitute $$ y = 0 $$ into the equation.

$$
2x - 3(0) = 12
$$

**Step 2:** Simplify the equation.

$$
2x - 0 = 12 \
2x = 12
$$

**Step 3:** Solve for $$ x $$.

$$
x = \frac{12}{2} \
x = 6
$$

**Solution:** When $$ y = 0 $$, $$ x = 6 $$.

### Summary

- **When $$ x = 0 $$:** $$ y = -4 $$
- **When $$ y = 0 $$:** $$ x = 6 $$

These points represent the x-intercept and y-intercept of the line defined by the equation $$ 2x - 3y = 12 $$.
When $$ x = 0 $$, $$ y = -4 $$. When $$ y = 0 $$, $$ x = 6 $$.

In the equation , solve for when and solve for when .

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