How can I solve systems of linear equations using the addition method?

AI Thread Summary
To solve systems of linear equations using the addition method, start by manipulating the equations to eliminate one variable. In the provided example, the first equation can be multiplied by a negative to facilitate the elimination of variable b. After adjusting the equations, add them together to simplify and solve for the remaining variable. This method relies on aligning coefficients to cancel out one variable effectively. Understanding this process is crucial for solving similar systems of equations.
elizavikki
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Can anyone help me to learn how to solve systems of linear equations?
{-5x-5y=-5
{-40x-3y=2

How do I go about doing this using the addition method?
 
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a+b=c
2a+b=3c

Eliminate either a or b. Since b is easier to get rid of, multiply either the 1st or 2nd equation by a negative. Then simply add straight down as you would normally.

Where is your work? I'm not going to work your problem, just giving you an example. So figure it out from there.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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