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

[manal950]

Hi all ..

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

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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
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-105 = -95 a
a = 1.1

is that correct ... ?

 

[dikmikkel]

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)

 

[azizlwl]

Correct. Called Gaussian Elimination.

 

[manal950]

thanks so much ..

 

[asteriatic]

I would suggest approaching this problem using the elimination method. This involves manipulating the equations to eliminate one variable and then solving for the other.

For example, in equation 1, we can subtract 10a from both sides to get:
12.5 - 10a = W0

We can then substitute this expression for W0 into equation 2:
20 = 10(12.5 - 10a) + 5a

Simplifying, we get:
20 = 125 - 95a

Solving for a, we get:
a = 1.1

We can then substitute this value back into either equation to solve for W0.

Using this method, we can find the values of a and W0 without having to multiply or add the equations. This approach may be more efficient and accurate.

However, your method also appears to be correct. It is always important to double check your calculations and make sure that your solution satisfies both equations. Great job on solving the equations!