How do you solve #5x - 2y = 10# and #3x + 2y = 6# using substitution?

1 Answer
May 25, 2018

Answer:

#x=2 and y=0#

Explanation:

I wonder why you would want to solve this by substitution when elimination is an easier and more obvious method because of the #-2y and +2y # terms.?

Make a single variable the subject:
#3x +2y =6 " "rarr 2y = 6-3x" "rarr color(blue)(y = 3-(3x)/2)#

Substitute this expression for #y# in the first equation:

#5x -2color(blue)(y) =10#

#5x -2(color(blue)(3-(3x)/2)) =10#

#5x -6+3x =10#

#8x = 16#

#x =2#

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

#y=0#

Compare the Elimination method

#" "5x-2y=10" "....A#
#" "ul(3x+2y =6)" ".....B#
#" "8x " "=16" "larr A+B#
#color(white)(xxxxx.x) x=2#

Substitute in #B#

#3x+2y=6#
#3(2)+2y=6#
#cancel6+2y = cancel6#
#y=0#