Can you check if this problem is not possible to be solved?

Question

I keep doing this problem and my values keep canceling themselves out? So I was wondering if this is not possible to be solved. Can you do it and tell me what you get? If you are able to solve it can you give me a quick guide on how you got to your answer, thanks!

Here it is:

2x+3y=-2
4y+2z=-10
3x+5z=1

Thanks for helping!

yes, I'm trying to find x,y, and z

Answer 1

Multiply the first equation by 3 and the third equation by 2. This will get both with 6x:
6x + 9y = -6
6x + 10z = 2

Subtract to cancel the x terms and you will get:
9y - 10z = -8

Your second equation is also just y and z. If you multiply by 5, you'll get 10z in both:
4y + 2z = -10
20y + 10z = -50

Add this to the last equation to cancel the z terms:
20y + 10z = -50
9y - 10z = -8

29y = -58
y = -58/29
y = -2

You have solved for y, now substitute this into another equation to solve for z:
4(-2) + 2z = -10
-8 + 2z = -10
2z = -2
z = -2/2
z = -1

Finally solve for x by substituting again:
2x + 3y = 2
2x + 3(-2) = -2
2x - 6 = -2
2x = 4
x = 2

The final answer is:
x = 2
y = -2
z = -1

Answer 2

It can be solved because you have 3 equations with 3 unknowns.

2x + 3y + 0z = -2

0x + 4y + 2z = -10

3x + 0y + 5z = 1

Now you should have been taught how to solve such, so I am not going to do the work for you. If you are using the matrix and determinate method, then I have given you the missing pieces of the puzzle.

Otherwise, get x in terms of y and z with two of the equations and plug these into the 3rd equation to solve for x...once you solve x you can then find y and z.

Answer 3

2x + 3y = - 2
2x = - 3y - 2
x = - 1.5y - 1

4y + 2z = - 10
4y = - 2z - 10
y = - 1/2z - 2.5

3(- 1.5[- 1/2z - 2.5] - 1) + 5z = 1
3(0.75z + 3.75 - 1) + 5z = 1
3(0.75z + 2.75) + 5z = 1
2.25z + 8.25 + 5z = 1
7.25z = - 7.25
z = - 1

y = - 1/2(- 1) - 2.5
y = 1/2 - 2.5
y = - 2

x = - 1.5(- 2) - 1
x = 3 - 1
x = 2

Answer: x = 2, y = - 2, z = - 1

Proof (substitute x, y & z in each of the original equation):
2(2) + 3(- 2) = - 2
4 - 6 = - 2

4(- 2) + 2(- 1) = - 10
- 8 - 2 = - 10

3(2) + 5(- 1) = 1
6 - 5 = 1

Answer 4

It looks like other folks have given you all the steps above. I hope that helps you spot your error.

I recommend using QuickMath (see http://www.quickmath.com) as a way to check your own answers. I just cut and pasted your equations into the advanced mode for the equation solver and it gave the solution x=2, y=-2 z=-1 immediately.

Don't misunderstand me -- QuickMath is not the way to DO your homework (you won't learn how to do it yourself that way) but it is an excellent tool for checking answers.

Answer 5

x = 2
y = -2
z = -1

The answer hasn't changed since the last time you asked!

Answer 6

Is this a system of equations for which you need to solve for x, y, and z?