SOLUTION: {{{system(-10x - 11y + 7z = 145,
7x - 4y - 3z = 53,
-5x - y = 146)}}}
I need to solve this using any method. Id like to see the steps and the correct
answer. I thi
Algebra ->
Coordinate Systems and Linear Equations
-> SOLUTION: {{{system(-10x - 11y + 7z = 145,
7x - 4y - 3z = 53,
-5x - y = 146)}}}
I need to solve this using any method. Id like to see the steps and the correct
answer. I thi
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Question 160537:
I need to solve this using any method. Id like to see the steps and the correct
answer. I think maybe I should start by multiplying the 3rd equation by 2 and
then subtract it from the 1st equation? I'm trying to make sense of this but I
just cant figure it out. I really appreciate your time. Thank you. Found 2 solutions by vleith, Edwin McCravy:Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website! If you know matrices, you can use that. But I suspect you are not there yet.
So, you might try substitution.
I would start with equation 3. Use it to find y in terms of x
You can then substitute that value for y into both equations 1 and 2.
Simplify this to get an equation with just x and z in it
Use it to find x in terms of z
Simplify this one too and get an equation with just x and z.
Substitute the z value in this last equation with the "z in terms of x" from the earlier equation.
You now have one equation with only x and constants in it.
Solve for x.
Niw use this value of x and the equation with z in terms of x to find z.
Then use x and z in any of the equations to solve for y (I would use the third original equation since it has only x and y in it)
That would work, but it would be the best way.
First you should observe that z is already eliminated
from the third equation, so you should eliminate z
from the first two equations:
To eliminate z from the first two equations:
Multiply the first equation by 3 and the second equation
by 7, then add them:
3[-10x - 11y + 7z = 145]
7[ 7x - 4y - 3z = 53]
-30x - 33y + 21z = 435
49x - 28y - 21z = 371
19x - 61y = 806
Now we take the third original equation with
this equation and solve this system:
We can do this by substitution:
Solve the first equation for y:
Substitute for in
Substitute that into
Now substitute and into
either one of the first two original equations.
Edwin
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