What are the solution(s) of the system of equations 2x+y=1, x-y=3?

1 Answer
Oct 13, 2015

Answer:

#{(x = 4/3), (y = -5/3) :}#

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 #y#-term will cancel out. This will allow you to find the value of #x#.

#{(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 #x# with its determined value to get the value of #y#.

#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) :}#