Question

Solve the system

x+y=54
x-5y=0
A. (-45, -9)
B.(45, 9)
C. (9, 45)
D. (45, 9)

Answer 1

`\displaystyle \\ \begin{cases} x+y = 54 \\ x-5y = 0~~~~~| \cdot (-1) \end{cases} \\ \\ \\ \begin{cases} x+y = 54 \\ -x+5y = 0 \end{cases} \\ \texttt{-------------- gather equations} \\ .~~/~~~~~6y = 54 \\ \\ y = (54)/(6) = \boxed{9} \\ \\ x = 54 - y = 54 - 9 = \boxed{45} \\ \\ \texttt{Problem solution: } \boxed{x = 45 ~~ and ~~ y = 9 }`