Question

Solve the following system of equations:

2x - y + z = -3

2x + 2y + 3z = 2

3x - 3y - z = -4

Answer 1

(1, 3, 2)
(-1, 3, 2)
(1, -3, 2)
(1, 3, -2)

Answer 2

@triciaal @whpalmer4 @tkhunny

Answer 3

does anyone know?

Answer 4

I know the answer.

And can tell you if you want to check your work.

Answer 5

yes please

Answer 6

I solved it using matrix analysis on my calculator and the answer is D.

But I suggest you plug the values into the equation to verify they are correct.

Answer 7

ok thank you

Answer 8

\[2x - y + z = -3\]\[

2x + 2y + 3z = 2\]\[

3x - 3y - z = -4\]

First add the first and third equations together, as they contain \(z\) with equal but opposite coefficients:
\[2x-y+z=-3\]\[3x-3y-z=-4\]-----------------\[5x-4y=-7\]

Next, add the first equation (multiplied by \(-3\)) and the second equation together:
\[-6x+3y-3z=9\]\[2x+2y+3z=2\]-------------------\[-4x+5y=11\]

Now you have two equations in 2 unknowns.

\[5x-4y=-7\]\[-4x+5y=11\]Multiply the first equation by \(4\) and the second by \(5\) and add them together:\[20x-16y=-28\]\[-20x+25y=55\]-------------------\[9y=27\]\[y=3\]

Now work backward through the equations to find \(x\) and \(z\):

\[5x-4y=-7\]\[5x-4(3) = -7\]5x-12=-7\]\[5x=5\]\[x=1\]

\[2x-y+z=-3\]\[2(1)-3+z=-3\]\[z=-2\]

answer is \((1,3,-2)\)

Important to check the answer by plugging it into all of the formulas and making sure it works for all of them, as it is possible to get "answers" that make some of the equations true while others are false.

Answer 9

Great job! I was both too tired and too lazy to do this last night. I apologize.