How do you solve the system of equations: 5x - 2y = 23 ; 5x + 2y = 17?

1 Answer
Aug 14, 2015

Answer:

The solutions are
#color(blue)(x=4,y=-3/2#

Explanation:

#5x - color(blue)(2y) = 23#.........equation #(1)#
# 5x + color(blue)(2y) = 17#.......equation #(2)#

Solving through elimination.
Adding the equations results in elimination of #color(blue)(2y#:
#5x - cancel(color(blue)(2y)) = 23#
# 5x + cancel(color(blue)(2y)) = 17#

#10x=40#
#color(blue)(x=4#

Now finding #y# from equation #1#

#5x -2y = 23#

#5x - 23=2y#

#20-23=2y#
#-3=2y#

#color(blue)(y=-3/2#