Question

For each system through the best description of a solution if applicable give the solution

Answer 1

System A

$\begin{gathered} -x+5y-5=0 \\ x-5y=5 \end{gathered}$

solve the second equation for x

$x=5+5y$

replace in the first equation

$\begin{gathered} -(5+5y)+5y-5=0 \\ -5-5y+5y-5=0 \\ -10=0;\text{FALSE} \end{gathered}$

The system has no solution.

System B

$\begin{gathered} -X+2Y=8 \\ X-2Y=-8 \end{gathered}$

solve the second equation for x

$x=-8+2y$

replace in the first equation

$\begin{gathered} -(-8+2y)+2y=8 \\ 8-2y+2y=8 \\ 8=8 \end{gathered}$

The system has infinitely many solutions, they must satisfy the following equation:

$\begin{gathered} -x+2y=8 \\ 2y=8+x \\ y=\frac{8}{2}+\frac{x}{2} \\ y=\frac{x}{2}+4 \end{gathered}$