How do you solve #x+y=3#; #x+2y=5#?

1 Answer
Apr 7, 2015
  • We can solve for the values of x and y using the 'Elimination by Substitution' method.

  • Let's number the equations first:
    #x+y=3# ------(1)
    #x+2y=5#------(2)

In (1), by transposing #y# to the other side, we get
#x= 3 - y#
Substituting this value of #x# in (2), we get
#(3-y)+2y = 5#
#3+y=5#
#y=5-3#
#y=2#
Here, we eliminated #x# by substituting its value in (2)

  • We Substitute this value of #y# in (1) to get
    #x+2=3#
    #x=3-2#
    #x=1#

  • The Solution for the equations (1) and (2) is:
    #x=1 , y=2#

  • Once we arrive at a solution, it is a good idea to VERIFY our answer

Substituting #x=1 , y=2# in (1) we get
Left Hand Side: #x+y = 1+2 = 3#(Right Hand Side)

Substituting #x=1 , y=2# in (2) we get
Left Hand Side: #x+y = 1+(2*2) = 5#(Right Hand Side)

We have verified our answer, and we can be sure that it's correct.