What are the solution(s) of the system of equations 2x+y=1, x-y=3?
1 Answer
Oct 13, 2015
Explanation:
Your system of equations looks like this
#{(2x + y = 1), (x - y = 3) :}#
Notice that if you add the left-hand sides and the right-hand sides of the two equations separately, the
#{(2x + y = 1), (x - y = 3) :}#
#color(white)(x)stackrel("----------------------------")#
#2x + color(red)(cancel(color(black)(y))) + x - color(red)(cancel(color(black)(y))) = 1 + 3#
#3x = 4 implies x= color(green)(4/3)#
Pick one of the two equations and replace
#4/3 - y = 3#
#4 - 3y = 9#
#-3y = 5 implies y = color(green)(-5/3)#
Therefore, the solution set for this system of equations is
#{(x=4/3), (y = -5/3) :}#