How do you solve the following system?: # x + 2y = 6 , 2x - 3y = 5 #

1 Answer

Answer:

#x=4 and y=1#

Explanation:

#x +2y =6" " " "(1)#
#2x + 3y =5" " " "(2)#

Multiply equation #(1)# by #3# and equation #(2)# by #2#,

#3 xx (x +2y=6) #2 xx (2x -3y=5)#

Therefore,

#3x + 6y = 18" " " "(3)#
#4x - 6y = 10" " " "(4)#

Add equation #(3)# to equation #(4)#

#7x+0=28#

Make #x# the subject of the equation

#x=28/7#

#x=4#

Substitute the value of #x# in equation #(1)#

#x +2y =6#

#4+2y =6#

Collect like terms

#2y= 6-4#

#2y=2#

Divide through by #2# to make #y# the subject of the equation

#y=1#

Ans:

#x=4 and y=1#