How do you solve the system of equations #3x - 4y = - 6# and #x - 5y = 9#?

2 Answers
Sep 3, 2017

We have,

#3x - 4y = -6#
#x - 5y = 9#

Multiplying the second equation with 3 and subtracting from the first,

#-4y + 15y = -33#
#implies 11y = -33#
#implies y = -3#

Substituting this value in the second equation,

#x = 9 + 5(-3)#
#implies x = 9 - 15#
#implies x = -6#

Thus, the solution is #(-6,-3)#.

Sep 3, 2017

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

Explanation:

Given
[1]#color(white)("XXX")3x-4y=-6#
[2]#color(white)("XXX")x-5y=9#

Multiplying [2] by #3# (to make the coefficient of #x# the same as in [1]
[3]#color(white)("XXX")3x-15y=27#

Subtracting [3] from [1]
[4]#color(white)("XXX")11y=-33#

Dividing both sides of [4] by #11#
[5]#color(white)("XXX")y=-#

Substituting #3# for #y# in [1]
[6]#color(white)("XXX")3x-4xx(-3)=-6#

Simplifying
[7]#color(white)("XXX")3x=-6-12#

[8]#color(white)("XXX")3x=-18#

[9]#color(white)("XXX")x=-6#

Therefore #(x,y)=(-6,-3)#