We are given the linear systems of equations given below:
#3x -y = -6# #color(blue)(Eqn.1)#
#4x +3y = 29# #color(blue)(Eqn.2)#
Multiply #color(blue)(Eqn.1)# by #3#
Hence, #color(blue)(Eqn.1)# yields #color(blue)(Eqn.3)#
#9x -3y = -18# #color(blue)(Eqn.3)#
#4x +3y = 29# #color(blue)(Eqn.2)#
When we add #color(blue)(Eqn.3)# and #color(blue)(Eqn.2)# we get
#9x -cancel(3y) = -18# #color(blue)(Eqn.3)#
#4x +cancel(3y) = 29# #color(blue)(Eqn.2)#
#rArr 13x = 11#
Therefore, #color(red)(x = 11/13)#
Substitute this value of #color(red)(x)# in #color(blue)(Eqn.1)#
#3x -y = -6# #color(blue)(Eqn.1)#
#rArr 3(11/13) - y = -6#
#rArr (33/13) - y = -6#
#rArr - y = -6 - (33/13)#
#rArr - y = (-78 - 33)/13#
#rArr - y = -111/13#
Divide both sides by #-1# to get
#rArr y =111/13#
Hence, our final solutions are : -
#color(red)[(x = 11/13) and (y = 111/13)# OR
We can simplify the fractions and write the solutions as
#color(red)[(x ~~ 0.8) and (y ~~ 8.5)#
