How do you solve the system #5x + y = 13# & #2x + 6y =22#?

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Answer 1 · 2017-01-30T13:31:26

#"the answer is x=2 and y=3"#

#5x+y=13 " (1)"#
#2x+6y=22" (2)"#

#"let us multiply the both sides of equation (1) by 6"#
#color(red)(6.)(5x+y)=color(red)(6.)13#
#30x+6y=78" (3)"#

#"subtract equation (2) from equation (3)"#
#30x+6y-(2x+6y)=78-22#
#30xcancel(+6y)-2xcancel(-6y)=56#
#28x=56#

#x=56/28#

#color(green)(x=2);#

#"now use (1) or (2)"#

#5 . color(green)(2)+y=13#
#10+y=13#

#y=13-10#

#y=3#