Identify a solution to this system of equations: ) -4x+3y=23 x-y=-7 a. (-5,2) b (-2,5) c (-3,4) d. (4,-3)

To solve the system of equations, we can use the method of substitution or elimination. Here, we'll use the elimination method.First, let's add the two equations together:\[\begin{aligned}-4x + 3y &= 23 \\x - y &= -7 \\\hline-3x + 2y &= 16\end{aligned}\]Now, we can solve for $x$:\[-3x + 2y = 16\]Divide both sides by -3:\[x = \frac{2y}{3} - \frac{16}{3}\]Now, substitute this expression for $x$ into the second equation:\[\frac{2y}{3} - \frac{16}{3} - y = -7\]Multiply through by 3 to clear the fraction:\[2y - 16 - 3y = -21\]Combine like terms:\[-y = -5\]Divide both sides by -1:\[y = 5\]Now, substitute $y = 5$ into the second equation to solve for $x$:\[x - 5 = -7\]Add 5 to both sides:\[x = -2\]So the solution is $(x, y) = \boxed{(-2, 5)}$, which corresponds to option b.