Can You Solve These Linear Equations for Variables a and w0?

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To solve the linear equations 12.5 = W0 + 10a and 20 = 10W0 + 5a, one approach is to manipulate the equations to eliminate variables. By multiplying the first equation by -10 and adding it to the second, the variable W0 can be removed, leading to the calculation of a. The resulting equation simplifies to -105 = -95a, yielding a = 1.1. Alternatively, isolating a in one equation and substituting it into the other or using Gaussian elimination are also valid methods. The discussion emphasizes the effectiveness of these algebraic techniques in solving for the variables.
manal950
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Hi all ..

How I can solve this two equations to get a and w0 ... ?
12 .5 = W0 + 10a ====== 1
20 = 10W0 + 5a ======= 2

--------------
this my trying ...
first I will multiply first equation with (-10) to remove the W0 then I will add both ..
-125 = -10W0 - 100 a
20 = 10W0 + 5a
--------------
-105 = -95 a
a = 1.1

is that correct ... ?
 
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Either you can isolate a in one of them and insert a in the other to isolate W0.
Or you could substract 2 times the equation below from the above yielding:
12.5-40 = W_0 - 20W_0 +10a -10a
Then a should be easy(insert W0)
 
Correct. Called Gaussian Elimination.
 
Last edited:
thanks so much ..
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

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