How do you solve the system of equations #4x = 2+ 2y# and #- \frac { 6} { 5} x + y = \frac { 27} { 5}#?

1 Answer
Nov 5, 2017

Answer:

#x = 37/8# and #y = 33/4#

Explanation:

#=>4x = 2 + 2y#

#=> 4x - 2y = 2# ………[1]

#=> -6/5x + y = 27/5#

Multiply both sides by #2#

#=> -12/5x + 2y = 27/5# ………[2]

Add equations [1] and [2]

#4x - 2y - 12/5x + 2y = 2 + 27/5#

#4x - 12/5x = 2 + 27/5#

#(4x × 5/5) - 12/5x = (2 × 5/5) + 27/5#

#(20x)/5 - (12x)/5 = 10/5 + 27/5#

#(20x - 12x)/5 = (10 + 27)/5#

#(8x)/5 = 37/5#

#x = 37/8#

Substitute #x = 37/8# in equation [1]

#4x - 2y = 2#

#(4 × 37/8) - 2y = 2#

#37/2 - 2y = 2#

#2y = 37/2 - 2#

#2y = 37/2 - (2 × 2/2)#

#2y = 37/2 - 4/2#

#2y = (37 - 4)/2#

#2y = 33/2#

#y = 33/4#