How do you solve -2x-9y=-25 and -4x-9y=-23?

2 Answers
Sep 5, 2015

Answer:

I found:
#x=-1#
#y=3#

Explanation:

I would add together the two equations (in columns) after multiplying the first by #-1# to get:
#{(color(red)(2x+9y=25)),(-4x-9y=-23):}# add together:
#-2x+0=2#
#x=2/-2=-1#
Substitute into the first equation:
#2-9y=-25#
#-9y=-27#
#y=27/9=3#

Sep 5, 2015

Answer:

#{(x=-1),(y=3):}#

Explanation:

Your system of equations looks like this

#{(-2x-9y = -25), (-4x-9y = -23) :}#

Multiply the first equation by #(-1)# to get

#-2x-9y = -25| * (-1)#

#2x + 9y = 25#

The system now looks like this

#{(2x+9y = 25), (-4x-9y = -23) :}#

Add the left-hand sides and the right-hand sides of the two equations seprately to get

#2x + color(red)(cancel(color(black)(9y))) - 4x - color(red)(cancel(color(black)(9y))) = 25 - 23#

#-2x = 2 implies x= 2/((-2)) = -1#

Take this value of #x# into one of the two equations to get the value of #y#

#-2 * (-1) - 9y = -25#

#2 - 9y = -25#

#-9y = -27 implies y = ((-27))/((-9)) = 3#

The solution set to this system of equations is #x = -1# and #y = 3#.