How do you solve the system of equations #-x-y=15# and #-8x+8y=24#?

1 Answer
Aug 4, 2016

Answer:

#{(x=-9), (y=-6) :}#

Explanation:

The system of equations given to you looks like this

#{( -color(white)(1)x - color(white)(1)y = 15), (-8x + 8y = 24) :}#

Notice that one equation features #y# with a positive sign and the other has it with a negative sign. This means that if you get the coefficients to match, you can add the two equations and get rid of the #y# terms.

To do that, multiply the first equation by #8#

#{( -color(white)(1)x - color(white)(1)y = 15" " | xx 8), (-8x + 8y = 24) :}#

this will get you

#{ ( -8x - 8y = 120), (-8x + 8y = color(white)(1)24) :}#

Now you're ready to add the two equations

#{ ( -8x - 8y = 120), (-8x + 8y = color(white)(1)24) :}#
#color(white)(aaaaaaaaaaaaaaa)/color(white)(a)#

#-8x + (-8x) - color(red)(cancel(color(black)(8y))) + color(red)(cancel(color(black)(8y))) = 120 + 24#

#-16x = 144 implies x = 144/(-16) = -9#

Take this value of #x# into the first equation and find the value of #y#

#- (-9) - y = 15#

#-y = 15 - 9 implies y = -6#

Therefore, the two solutions to your system of equations are

#{(x=-9), (y=-6) :}#