How do you solve the system of equations #-6x + 5y = 8# and #x + 5y = - 13#?

2 Answers
Dec 19, 2017

#x=-3 and y = -2#

Explanation:

Let,
#-6x + 5y = 8# ----- (1)

#x + 5y = - 13#----(2)

(2)#=> x = -13 -5y#

Substitute this value of #x# in (1):

(1)#=> -6(-13 -5y) + 5y = 8#

#=> 78 + 30y +5y =8#

#=> 35y = 8-78#

#=> y = -70/35 = -2#

#therefore y = -2#

Now substitute this value in the expression of #x#:

#=> x = -13 -5y#

#=> x = -13 -5(-2)#

#=> x = -13 +10#

#therefore x = -3#

Answer: #x= -3 and y = -2#

Dec 19, 2017

#x =-3 and y=-2#

Explanation:

Notice that the #y# terms both have the same coefficient.

Subtracting the equations will therefore eliminate the #y# terms.

#" "x" "color(red)(+" "5y)" " =-13" "............................ A#
#-6x" "color(red)(+" "5y)" " =8" ".......................... B#

Subtract #A - B" "# (change the signs of #B#)

#" "x" "+" "5y" " =-13" "color(white)(xxxxxxxxx)A#
#ul(color(blue)(+)6x" "color(blue)(-)" "5y" " =color(blue)(-)8)" "color(white)(xxxxxxxxx)B#
#" "7xcolor(white)(xxxxxxxxx) =-21" "color(white)(xxxxxxxxxx)C" "larr div 7#
#" "xcolor(white)(xxxxxxxxx) =-3#

Substitute #-3 " for " x# in #A#

#-3+5y =-13#
#" "5y = -13+3#
#" "5y=-10#
#" "y=-2#

An alternative method is to equate the #y# terms.
Transpose the equations to isolate #5y# in each:

#5y = -13-x" and "5y =8+6x#

We know that #" "5y=5y#

Therefore: #" "6x+8 = -13-x" "larr# now solve for #x#

#6x+x = -13-8#
#" "7x = -21#
#" "x =-3#

Then proceed as described above to get #y=-2#

Check in #B#
#-6x+5y#
#=-6(-3)+5(-2)#
#=18-10#
#=8" "larr# the answer is the same as the RHS