How do you solve the following system?: #9x -5y =21, -x -y = -2#

1 Answer
Jun 27, 2018

Answer:

#(31/14,-3/14)#

Explanation:

Let's start with the second equation by dividing every term by #-1#. We now have the following system:

#color(blue)(9x-5y=21)#

#x+y=2#

Let's subtract #x# from both sides of the second equation. We get

#color(red)(y=-x+2)#

We can now plug this value into the blue equation. We get

#9x-5color(blue)((-x+2))=21#

Simplifying gives us

#9x+5x-10=21#

#=>14x=31#

#=>x=31/14#

We can plug this into the red equation to get

#y=-color(red)(31/14)+28/14#

#y=-3/14#

Therefore, our solutions are

#(31/14,-3/14)#

Hope this helps!