Answer: x=27 y=4
Step-by-step explanation:
Let the larger of two numbers is x and the smaller of two numbers is y
Hence,
[tex]\displaystyle\left \{ {x-5y=7} \atop {x+y=31}} \right.\\\\\left \{ {{x-5y=7} \atop {x+y-y=31-y}} \right. \\\\\left \{ {{x-5y=7\ \ \ \ \ (1)} \atop {x=31-y}\ \ \ \ (2)} \right. \\[/tex]
Substitute equation (2) into equation (1):
[tex]31-y-5y=7\\31-6y=7\\31-6y+6y=7+6y\\31=7+6y\\31-7=7+6y-7\\24=6y\\[/tex]
Divide both parts of the equation by 6:
[tex]4=y\\Hence,\\x=31-4\\x=27[/tex]
