Question

If it can be determined, what point, (x, y), lies on both of the lines indicated below?4x+2y=162x+y=4A. (-2,8)B. (2,4)C. (6, -8)D. No solution exists for this system

Answer 1

The given system is

$\mleft\{\begin{aligned}4x+2y=16 \\ 2x+y=4\end{aligned}\mright.$

We multiply the second equation by -2, then we sum equations

$\begin{gathered} \mleft\{\begin{aligned}4x+2y=16 \\ -4x-2y=-8\end{aligned}\mright. \\ 0x+0y=8 \\ 0=8 \end{gathered}$

Since 0 is not equal to 8, we deduct that the system has no solutions.

Therefore, the answer is D.