How do you solve the following system: #5x-9y=-2, 7x-2y= -67 #?

1 Answer
Apr 10, 2018

Answer:

#(x,y)=( -11 16/53,-6 3/53)#

Explanation:

Given
[1]#color(white)("XXX")5x-9y=-2#
[2]#color(white)("XXX")7x-2y=-67#

Convert to equivalent equations with the same coefficient for #y#
by multiplying [1] by #2#
and multiplying [2] by #9#
[3]#color(white)("XXX")10x-18y=-4#
[4]#color(white)("XXX")63x-18y=-603#

Subtract [3] from [4] to eliminate the #y# term
[5]#color(white)("XXX")53x=-599#

Divide both sides of [5] by #53#
[6]#color(white)("XXX")x=-599/53= -11 16/53#

We could substitute #-599/53# for #x# in one of the given equation (either one) and solve for #y#
or repeat a similar process to the one above to eliminate the #x# factors:

Multiply [1] by #7# and [2] by #5#
[7]#color(white)("XXX")35x-63y=-14#
[8]#color(white)("XXX")35x-10y=-335#

Subtract [7] from [8]
[9]#color(white)("XXX")53y=-321#

Divide both sides of [9} by #53#
[10]#color(white)("XXX")y=-321/53=-6 3/53#