How do you solve the system of equations: x+2y=3, 3x-y= -5?

1 Answer
Aug 5, 2015

Answer:

#(x,y) = (-1,2)#

Explanation:

[1]#color(white)("XXXX")##x+2y=3#
[2]#color(white)("XXXX")##3x-y=-5#

Multiply [2] by 2 (so the coefficient of #y# corresponds to that in [1])
[3]#color(white)("XXXX")##6x-2y=-10#

Add [1] and [3] (eliminating the #y# term)
[4]#color(white)("XXXX")##7x = -7#

Divide [4] by 7
[5]#color(white)("XXXX")##x = -1#

Substitute #(-1)# for #x# in [1]
[6]#color(white)("XXXX")##(-1)+2y = 3#

Add 1 to both sides of [6]
[7]#color(white)("XXXX")##2y=4#

Divide both sides by 2
[8]#color(white)("XXXX")##y=2#