![To solve the system of equations:
1. **Equations:**
\[
4x + y = 17 \quad \text{(1)}
\]
\[
-6x - y = -23 \quad \text{(2)}
\]
2. **Rearranging equation (2):**
\[
-6x - y = -23 \implies y = -6x + 23 \quad \text{(3)}
\]
3. **Substituting (3) in (1):**
\[
4x + (-6x + 23) = 17
\]
\[
4x - 6x + 23 = 17
\]
\[
-2x + 23 = 17
\]
\[
-2x = 17 - 23
\]
\[
-2x = -6
\]
\[
x = 3
\]
4. **Finding y using (3):**
\[
y = -6(3) +](https://theinternetioimages-f2htc2ggcrath6d7.z01.azurefd.net/$web/askai/7ebd6982-0c54-4ee4-9b3c-1d24395c2b8e.webp)
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Question: Solve the following system of equations 4x+y=17 -6x-y=-23
Asked by aus
Let's solve the system of equations: \[ \begin{align*} 1)\quad 4x + y &= 17 \\ 2)\quad -6x - y &= -23 \end{align*} \] Let's use **elimination**. Add both equations together to eliminate \( y \): \[ (4x + y) + (-6x - y) = 17 + (-23) \] Simplify: \[ 4x - 6x + y - y = 17 - 23 \\ -2x = -6 \] Now, solve for \( x \): \[ x = \frac{-6}{-2} = 3 \] Now substitute \( x = 3 \) into equation (1): \[ 4(3) + y = 17 \\ 12 + y = 17 \\ y = 17 - 12 = 5 \] **Solution:** \[ \boxed{x = 3,\quad y = 5} \] If you want them as an ordered pair: \[ \boxed{(3,\ 5)} \]
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