Ask AI: Solve the following system of equations 4x+y=17 -6x-y=-23

Let's solve the system of equations step by step: Given: 1. \(4x + y = 17\) 2. \(-6x - y = -23\) Let's solve by **addition** (elimination method): First, add the two equations together: \[ (4x + y) + (-6x - y) = 17 + (-23) \] \[ 4x + y - 6x - y = 17 - 23 \] \[ (4x - 6x) + (y - y) = -6 \] \[ -2x = -6 \] Now solve for \(x\): \[ x = \frac{-6}{-2} = 3 \] Now substitute \(x = 3\) back into the **first equation**: \[ 4x + y = 17 \] \[ 4(3) + y = 17 \] \[ 12 + y = 17 \] \[ y = 17 - 12 = 5 \] **Solution:** \[ \boxed{x = 3, y = 5} \] If you'd like to double-check, substitute \(x = 3, y = 5\) into the second equation: \[ -6x - y = -23 \] \[ -6(3) - 5 = -18 - 5 = -23 \] This checks out!