How do you solve the following system: #8x-3y=3, x+3y=3 #?

2 Answers
May 13, 2018

Answer:

This ordered pair is #(2/3, 7/9)# or #(0.bar6, 0.bar7)#.

Explanation:

Use the elimination method, and then substitution to solve. Line up the two equations, one on top of the other:

#8x - 3y = 3#
#color(white)(8)##x + 3y = 3#

Now add them together, and notice that #y# will be eliminated because #-3y + 3y = 0#:

#8x color(blue)(- 3y) = 3#
#color(white)(8)##x color(blue)(+ 3y) = 3#


#color(white)(x)9x color(white)(+ 0y) = 6#

#9x = 6#

#x = 6/9 rarr 2/3#

Now substitute that value for #x# into another equation, and solve for #y#:

#x + 3y = 3#

#2/3 + 3y = 3#

#2 + 3(3)y = 3(3)#

#2 + 9y = 9#

#9y = 7#

#y = 7/9#

So this ordered pair is #(2/3, 7/9)#. As a repeating decimal, the coordinates are #(0.bar6, 0.bar7)#.

May 13, 2018

Answer:

Solution: # x= 2/3 and y= 7/9#

Explanation:

#8 x-3 y=3 ; (1) , x +3 y =3; (2)# , adding equation (1)

and equation (2) we get, # 9 x = 6 :. x = 6/9 or x= 2/3#

Putting #x=2/3# in equation (2) we get, #2/3 +3 y =3; # or

#3 y =3- 2/3 or 3 y = 7/3 or y = 7/9 #

Solution: # x= 2/3 and y= 7/9# [Ans]