3. Which system of equations has a solution of \( (3,-4) ? \) A. \( \left\{\begin{array}{c}y=2 x-10 \\ y=x-1\end{array}\right. \) B. \( \left\{\begin{array}{l}x+y=-1 \\ y=-4 x+8\end{array}\right. \) C. \( \left\{\begin{array}{l}y=2 x \\ y+3 x=5\end{array}\right. \) D. \( \left\{\begin{array}{l}y-5 x=-17\end{array}\right. \)

To find out which system of equations has the solution \( (3, -4) \), we need to substitute \( x = 3 \) and \( y = -4 \) into each option. Let’s break it down: For option A: - First equation: \( y = 2(3) - 10 = 6 - 10 = -4 \) (True) - Second equation: \( y = 3 - 1 = 2 \) (False) Option A does not work. For option B: - First equation: \( 3 + (-4) = -1 \) (True) - Second equation: \( -4 = -4(3) + 8 \implies -4 = -12 + 8 \implies -4 = -4 \) (True) Option B works! For option C: - First equation: \( -4 = 2(3) = 6 \) (False) Option C does not work. For option D: - There’s only one equation: \( -4 - 5(3) = -4 - 15 = -19 \) (Does not show x or y equals anything) So, Option B is correct! In summary, the system of equations with the solution \( (3, -4) \) is given by option B.