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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