Sure, for these types of questions where we have two equations in two variables, we usually try to solve one equation for one variable and then substitute that into the second equation. Here, since the second equation, y = -5x + 22, is already solved for y, we can substitute this y into the first equation.
By substituting -5x+22 for y in the first equation, it transforms into:
-3(-5x + 22) - x = -10
which simplifies to:
15x - 66 - x = -10
and combines like terms to get
14x = 56.
From here, we isolate x by dividing both sides of the equation by 14:
x = 56/14
x = 4.
Now we've solved for x, we can substitute x = 4 into the second equation to find y:
y = -5*(4) + 22
y = -20 + 22
y = 2.
Therefore, the ordered pair that satisfies both equations is (4, 2).