#3x+4y=-2" (1)"#

#-2x-3y=1" (2)"#

#"expand both sides of equation (1) by 2;"#

#6x+8y=-4#

#"rearranging the equation :" 6x=-4-8y" "(3)#

#"expand both sides of equation 2 by 3;"#

#-6x-9y=3#

#"rearranging the equation :"6x=-9y-3" "(4)#

#"Both ;the left sides of equations (3) and (4) are equal" #

#color(red)(6x)=-4-8y#

#color(red)(6x)=-9y-3#

#"The right sides of equations can be written as equal"#

#-4-8y=-9y-3#

#9y-8y=-3+4#

#y=1#

#"now use (1) or (2)"#

#3x+4*1=-2#

#3x+4=-2#

#3x=-6#

#x=-6/3#

#x=-2#