Question

15 = 10x + 5y
x -2 -1 0 2 3
y

Answer 1

To find the values of \( y \) for the equation \( 15 = 10x + 5y \) given the values for \( x \) as \(-2, -1, 0, 2, 3\), we'll substitute each value of \( x \) into the equation and solve for \( y \).

### Step 1: Solve the equation for \( y \)

Starting from the original equation:
\[
15 = 10x + 5y
\]

Rearranging it gives:
\[
5y = 15 - 10x
\]
\[
y = \frac{15 - 10x}{5}
\]
\[
y = 3 - 2x
\]

### Step 2: Calculate \( y \) for each value of \( x \)

1. **When \( x = -2 \)**:
\[
y = 3 - 2(-2) = 3 + 4 = 7
\]

2. **When \( x = -1 \)**:
\[
y = 3 - 2(-1) = 3 + 2 = 5
\]

3. **When \( x = 0 \)**:
\[
y = 3 - 2(0) = 3 - 0 = 3
\]

4. **When \( x = 2 \)**:
\[
y = 3 - 2(2) = 3 - 4 = -1
\]

5. **When \( x = 3 \)**:
\[
y = 3 - 2(3) = 3 - 6 = -3
\]

### Summary of \( y \) values

- For \( x = -2 \), \( y = 7 \)
- For \( x = -1 \), \( y = 5 \)
- For \( x = 0 \), \( y = 3 \)
- For \( x = 2 \), \( y = -1 \)
- For \( x = 3 \), \( y = -3 \)

Here is a summary of the results:

\[
\begin{align*}
x & : -2, -1, 0, 2, 3 \\
y & : 7, 5, 3, -1, -3 \\
\end{align*}
\]