Question

Solve the system of equations.

10x+3y+2z=5
7x+6y+2z=20
4x−3y+3z=7

Can someone pls show me step by step

Answer 1

Here is what I would like to try
Combine the first and second equations with subtraction in order to eliminate the "z" terms:
10x+3y+2z=5
-(7x+6y+2z=20)
________________
3x -3y = -15
Then, divide both sides of this resulting equation by 3 to get:
x - y = -5
Add y to both sides to get the relationship:
x = y - 5
Now we know that x is 5 less than y, and we've gotten one step closer to solving for x, which in turn will allow us to solve for y and z.

Perhaps this will give you some idea of the methods you can use to go about this kind of problem. I won't solve the entire thing for you, but I'll be happy to give more guidance if needed. Please let me know if anything I demonstrated was confusing or if you need further help :)

Answer 2

ok here is where i mess up u chose the first and second equation, why not the first and third?

Answer 3

like, does it matter which i start first

Answer 4

and why did u subtract i thought we always had to add

Answer 5

thank you i'll keep trying , im in 11th grade and i think this year we'll start learning matrices, but this was just a review to begin

Answer 6

No problem. I'm willing to bet there's other users around who are more familiar with this topic than I am.
Maybe @mhanifa or @florisalreadytaken ? They tend to be rather active in the Mathematics section. In any case, I'm sure you'll be able to get the help you need :)

Answer 7

I think I have another idea.
Take the relationship (x = y - 5), which we got by combining the first and second equations.
Use that to replace x with (y-5) in the third equation:
4x−3y+3z=7
Becomes
4(y-5) -3y + 3z = 7
Distribute the 4 over y and -5 to get
4y - 20 - 3y + 3z = 7
Combine the common y terms:
-20 + y + 3z = 7
Add 20 to both sides:
y + 3z = 27
Subtract 3z from both sides:
y = 27 - 3z

Now we have a relationship between y and z.
Use this together with the relationship we found earlier between x and y, and we now have a way to substitute terms so that any equation will have only 1 variable. In this way, we should be able to solve for "z".
After that, we can solve for x and y.

Answer 8

I shall demonstrate using the first equation (though any of them would work:
10x+3y+2z=5
Use (x = y-5) to substitute x with (y-5):
10(y-5) + 3y + 2z = 5
Distribute the 10 to y and -5:
10y - 50 + 3y + 2z = 5
Add the common y terms:
13y - 50 + 2z = 5
Add 50 to both sizes:
13y + 2z = 55
Use (y = 27 - z) to substitute y for (27 - z)
13(27 - z) + 2z = 55
Distribute the 13 to 27 and z:
351 -13z + 2z = 55
Combine the common z terms:
351 - 11z = 55
Subtract 351 from both sides:
-11z = -296
Divide both sides by -11:
z = 296/11

And just like that, we have the value of z!
From here, finding the values of x and y should be a piece of cake, especially given those relationships we found earlier, (x = y-5) and (y = 27-z)
I trust I can leave that to you?

Answer 9

I think i did something really wrong i got mine a different way (the way my lesson said)

where i began with the first and last equation and for z I got 8

Answer 10

i did from the begginng
10x+3y+2z=5
-- 4x+-3y+3z=7

i aded the first and third to eliminate y

and got 14x+5z=12

Then 7x+6y+2z=20
and added 8x+-6y+6z=14

i got that by Multiplying it by 2 so that the y term

then i got 15x+8z=34
14x+5z=12
15x+8z=34

112x+40z=96
−75x−40z=−170

get that bymultiplying first equation by 8 and the second equation by −5

then here is where i get x, y and z

112x+40z=96
−75x−40z=−170

i added the equation and got 37x=74=x=-2

now 15(−2)+8z=34
=z=8

10(−2)+3y+2⋅8=5

and got y=3

Answer 11

but thats a really long tiring way

Answer 12

Hey, that's awesome! I didn't see any errors in your work, so I'm pretty confident you got the correct answer. Well done!
It does make me a little curious about what I did wrong, but that's not as important. I'm glad you were able to figure it out for yourself

Answer 13

I think I caught my error.
Back in this step, I substituted y with (27-z), but it should have been (27 - 3z):

Answer 14

Thank you for your time