How do you solve the following linear system: #x+y=1, 2x-3y=12#?

1 Answer
Mar 20, 2018

Answer:

#x= 3 and y = -2#

Explanation:

Let #x+y=1# ----------equation (1),

and # 2x-3y=12# -----------equation (2).

Multiply equation (1) by 2 and subtract the resultant equation from (2). This is eliminate one variable, i.e. #x# and we will get value of #y#. Then substitute the obtained value of #y# in any one original given equation to get value of #x#:

(1) # times 2 # - #(2) =>#

#=> 2x +2y - (2x -3y) = 2- 12#

#=> 2x +2y -2x +3y = -10#

#=> 5y = -10#

#=> y = -2#

Substituting #y# in (1)

(1) #=> x + (-2) = 1#

#=> x = 1+2 =3 #

#therefore x= 3 and y = -2#