How do you use elimination to solve the system of equations: 2x-4y=26 and 3x+2y=15?

1 Answer
May 31, 2016

Answer:

#color(green)(y= -3#
#color(green)(x=+7)#

Explanation:

Given:

#" "2x-4y=26" "#..............................Equation (1)
#" "3x+2y=15" "#..............................Equation (2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Multiply eqn(2) by 2 and then add

#" "2x-4y=26" ".............................. (1)#
#" "underline(6x+4y=30)" ".............................. (2_a)#
#" "8x+0y=56" "..............................(3)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Divide eqn(3) by 8

#color(green)(" "x=56/8=7)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Multiply eqn(1) by 3 and eqn(2) by 2
Then #"eqn"(1_a)-"eqn"(2_b)#

#6x-12y=78" "..........................................(1_a)#
#underline(6x+color(white)(.)4y=30)" "..........................................(2_b)#
#0x-16y=48" ".........................................(4)#

Divide both sides by #-16#

#color(green)(y=48/(-16) = -3)#