Answer:
-6x + 10y -2z
Explanation:
Let's first simplify the words a little bit for understanding:
Subtract A from B plus C.
Which is: (B + C) - A
Looks easy when written that way, right?
So how do you add equations? One way is to just stack them on top of each other like any other addition problem, right?
- x - 3y + 2z
- + -4x + 9y - 11z
That should look familiar from previous instruction or your textbook. So now just literally add the terms. You come out with negative 3 x's, 6 y's, and negative 9 z's:
-3x + 6y - 9z Make sure you understand how that's done.
That's the "sum of" the 2nd two equations. Now we need to subtract the 1st one from that. Just like adding equations, we can stack them and subtract:
- -3x + 6y - 9z
- - (3x - 4y - 7z)
Here I put the 2nd equation in parentheses because the subtraction will change all those signs and we need to be careful.
But once you've changed the signs you can add, right? This is what that would then look like:
- -3x + 6y - 9z
- + -3x + 4y + 7z
- -6x + 10y -2z <-- answer
The other way to do it, which you might find easier, is to use the form I derived above from the words:
(B + C) - A
And using whatever property that is, can't I remove the parentheses here? So:
B + C - A
(x - 3y + 2z) + (-4x + 9y - 11z) - (3x - 4y - 7z)
Then just go through and write them all outside of the parentheses, but be careful on that 3rd part, where the subtraction flips all the signs:
x - 3y + 2z - 4x + 9y - 11z - 3x + 4y + 7z
Then just add up all the x's and y's and z's:
-6x + 10y - 2z
Which is the same answer as before.
Good luck, and take care.