How do solve the following linear system?: # x-4y=-24 , x+y=-1 #?

1 Answer
Tony B
Jan 17, 2016

The lines cross at #(x,y)->(-28/5,+23/5)->(-5 3/5,+4 3/5)#

Explanation:

Given:
#color(white)(..)color(brown)(x-4y=-24)#......................(1)
#color(white)(..)color(brown)(x+y=-1)#..........................(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider equation (2)

Take the #y# over to the other side of the = and change its sign

#x=-1-y#............................................(3)

Using equation (3) substitute for #x# in equation (1) giving

#x-4y=-24" becomes "-> -1-y-4y=-24#

Multiply everything by (-1) to change the signs

#1+y+4y=24#

#1+5y=24#

Move the left hand side 1 to the right and change its sign

#5y=24-1" = "23#

Divide both sides by 5 giving

#color(green)(y=23/5)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substitute #y=23/5# in equation (2) giving:

#x+y=-1" becomes "->x+23/5=-1#

Move the #23/5# to the other side of = and change its sign

#x=-1-23/5 " = " -28/5#

#color(green)(x=-28/5)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So the lines cross at #(x,y)->(-28/5,23/5)->(-5 3/5,+4 3/5)#

Tony B

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