Solve using elimination.

10x + y = - 19

10x + 3y = - 17

Subtract 10x

10x + y = - 19

10x + 3y = - 17

You would get:

-2y = - 2

Two negatives make a positive number! Divide

y = 1

Plug in

10x + (1) = - 19

10x = - 20

Divide

x = - 2

Your solutions are

x = - 2

y = 1

we want to add the 2 equations to eliminate a variable

see which constants match

the x's both have 10

multiply the first equation by - 1

-10x-y=19

add that to the 2nd equation

-10x-1y=19

10x+3y=-17 +

0x+2y=2

so 2y=2 - > y=1

subsitute to find other number

10x+y=-19

10x+1=-19

10x=-20

divide both sides by 10

x=-2

the solution is (x, y) = (-2,1)