Solve equation by elimination:

2x + y = - 1

6x + y = - 21

Change the sign on the first one, making it - 2x - y = 1

Then combine the terms you have,

-2x-y=1

and

6x+y=-21

And this will give you

4x=20

Then solve that equation for x by dividing both sides by 4, giving you x=4

Then plug 5 into x's place in either of the original equations.

This is if you use the first equation

2 (5) + y=-1

Solve for y by simplifying

10+y=-1

Then subtract 10 from both sides

y=-11.

The final answer is x=5 and y=-11

Solve for y

2x+y=-1

y=-2x-1

Sub y = - 2x-1 into an equation and solve for x

6x-2x-1=-21

4x-1=-21

4x=-20

x=-5

Sub - 5 for x in either equation

2 (-5) + y=-1

-10 + y=-1

y=9

Check answer by substituting both solutions

6 (-5) + 9=-21

-30+9=-21

-21=-21

2 (-5) + 9=-1

-10+9=-1

-1=-1

x=-5, y=9