Please solve these equations

Question

x+y+z=-1, 3x-2y-4z=16, 2x-y+z=19

Answer 1

Here's a simpler problem that I hope will jog your memory.

x + 2y = 13

2x + y = 11

It doesn't matter if we solve for x or y first. We'll solve for y, which means we need to eliminate x. You could divide the bottom equation by 2 to get it in terms of x, but that would leave you with 1/2y and 11/2 which is awkward. Better is to multiply the top equation by 2. Now...

2x + 4y = 26

2x + y = 11

Subtract the bottom equation from the first

0x + 3y = (26-11) which is 3y = 15, so y = 5. Plug y =5 into any equation with x's and y's in it and solve for x.

Answer 2

I would put together all "like terms"=all totals.

You can get any amount of values because there's not enough imfo.

Answer 3

I won't solve this set for you, but I will tell you how to do it.

Subtract 3 times the first equation from the second equation.

Subtract 2 times the first equation from the third equation.

Now you will have a pair of simultaneous equations in y and z which you can solve by any convenient method, most likely elimination,

Answer 4

Follow the rules for combining equations and matrix operations will be simple later.

x + y + z = -1 [a]

3x - 2y - 4z = 16 [b]

2x - y + z = 19 [c]

The elimination method makes one coefficient either equal or opposite so that either subtracting or adding equations eliminates that term.

Add equations [a] and [c] {note: you could do others}

3x + 2z = 18 [d]

Add 2*{a] to equation [b]

5x - 2z = 14 [e]

Now, ass equation [d] to equation [e]

8x = 32 [f]

And solve for x:

x = 4

Plug that into either [d] or [e]

3(4) + 2z = 18

2z = 6

z = 3

Now plug the values for x and z into either [a], [b]. or [c] to get the value for y.

Be sure to check that [a], [b]. and [c] are satisfied using your results !!