What is the solution to the following system?: #-6x + 10y = 5, -2x + 3y = -1#

1 Answer
May 31, 2018

Answer:

#x=25/2#

#y=8#

Explanation:

Make #x# or #y# the subject and then substitute that in one of the equation.

#-6x+10y=5# -----> equation 1

#-2x+3y=-1# ------> equation 2

Lets make #x# the subject in equation 1:

#-6x+10y=5#

#-6x = 5-10y#

#x=-5/6+10/6y# ------> substitute #x# in equation 2

#-2x+3y=-1# ------> equation 2

#-2(-5/6 + 10/6y) + 3y = -1#

#5/3-10/3y+3y=-1#

#3y-10/3y = -1-5/3#

#(9y-10y)/3 = (-3-5)/3#

#-1/3y = -8/3#

#y = -8/3 xx (-3)#

#y=8#

Substitute #y=8# in equation 2 to get value of #y#.

#-2x+3y=-1# ------> equation 2
#-2x +3(8) = -1#

#-2x+24=-1#

#-2x = -1-24#

#-2x = -25#

#x=25/2#

Check the answer:

#-6x+10y=5# -----> equation 1

#-6(25/2) + 10(8) = 5 #-75+80 = 5# ----> correct