What is the solution of - 4x + y=6 and - 5x - y=21

We can eliminate one of the placeholders by adding the 2 eqations together

-4x-5x+y-y=21+6

-9x=27

divide both sdie sby 9

-x=3

multiply - 1

x=-3

subsitue - 3 for x

-4 (-3) + y=6

12+y=6

subtract 12 form both sides

y=-6

x=-3

y=-6

So,

We can eliminate the y's with Elimination by Addition.

(-4x + y) + (-5x - y) = 6 + 21

-9x + 0y = 27

-9x = 27

Divide both sides by - 9

x = - 3

Plug x into the equation

-4 (-3) + y = 6

12 + y = 6

Subtract 12 from both sides

y = - 6

Check

-4 (-3) + - 6 = 6

-4 (-3) - 6 = 6

12 - 6 = 6

6 = 6

This checks. The solution for this System of Simultaneous Linear Equations is the ordered pair (-3,-6).