How do you solve the following system?: 9x -5y =21, -x -y = -29x5y=21,xy=2

1 Answer
Jun 27, 2018

(31/14,-3/14)(3114,314)

Explanation:

Let's start with the second equation by dividing every term by -11. We now have the following system:

color(blue)(9x-5y=21)9x5y=21

x+y=2x+y=2

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

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

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

9x-5color(blue)((-x+2))=219x5(x+2)=21

Simplifying gives us

9x+5x-10=219x+5x10=21

=>14x=3114x=31

=>x=31/14x=3114

We can plug this into the red equation to get

y=-color(red)(31/14)+28/14y=3114+2814

y=-3/14y=314

Therefore, our solutions are

(31/14,-3/14)(3114,314)

Hope this helps!