Solve the equations simultaneously.
Firstly, choose 1 equation and make either #x# or #y# the subject.
#3x-6y=-9#
#3x=-9+6y#
#color(red)x=-3+2y# ------- (1) Let this be equation 1.
#-6color(red)x+10y=6# ------(2) Let this be equation 2.
Notice both equations have #x#?
Substitute (1) into (2).
#-6(-3+2y)+10y=6#
The #x# has been eliminated, and #y# can now be found.
#18-12y+10y=6#
#-12y+10y=6-18#
#-2y=-12#
#color(blue)(y=6)#
Since #y=6#, we can substitute this #y# value into (1).
#x=-3+2(6)#
#color(red)(x=9)#
When the #x# and #y# values are found, be sure to double check whether the answers satisfy the original equations.
When #y=6# and #x=9#,
#3x-6y=-9#
#3(9) - 6(6) = -9#
#27-36=-9#
#-9=-9#
Since both sides of the equation match, the answers are correct.
