I just cant solve this linear equation system..

Question

I need your help to solve this equation:

$$5000ps= 1500+ 100pw$$ $$1420pw= 3200+ 1000ps$$

$$80pa= 5050+ 2000ps+ 100pw + 20pa$$

I'm searching for pa, pw and ps.

Could someone help me in solving these linear equation.

Note - pw, pa and ps are variables

Answer 1

You could write your system as:

$-100 (pw) +5000 (ps) =1500$

$1420 (pw) -1000 (ps)=3200$

$-100 (pw) -2000 (ps) +60 (pa)=5050$

We could use a method called Gaussian Elimination, to make the process systematic (even without a computer). We need to create an augmented matrix of coefficients separate the right hand side by a vertical bar and perform row and column operations to convert the matrix to an equivalent matrix with only the value 1 in each diagonal entry and zeroes everywhere else. This makes the variables easy to get. The steps are as follows:

$pw=2.5$ $ps=0.35$ $pa=100.$

I have used This tool, since typing all this is too much for me.

Answer 2

The given equations are -

$$5000=1500+100$$ $$1420=3200+1000$$ $$80=5050+2000+100+20$$

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You can solve for $pa, ps \ and \ pw$ in the following way

• Multiply the second equation with $5$.

• Then solve first and second equation.

• You will get $pw = 2.5$.

• Now substitute $ pw = 2.5$ in either the first equation or the second equation to get $ps$. You will get $ps = 0.35$

• Substitue the value of $ps$ and $pw$ in the third equation to find the value of $pa$.

I would suggest you to try solving for $pa$ on your own. If you need any help, feel free to ask.