system of linear equations

marko

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Mar 12, 2006
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I see that the addition method is also called the elimination method. I don't understand which one (x or Y) to choose to eliminate first. Also,if you choose to multiple to create a cancellation, how do you determine what to multiply by? ex.
2x +5y =6
3x - 2y = 6x +2 This is a "you try it". I don't get how they eliminated the 6x to solve the system, as they put it. So many questions...so little time.
 
marko said:
I see that the addition method is also called the elimination method. I don't understand which one (x or Y) to choose to eliminate first. Also,if you choose to multiple to create a cancellation, how do you determine what to multiply by? ex.
2x +5y =6
3x - 2y = 6x +2 This is a "you try it". I don't get how they eliminated the 6x to solve the system, as they put it. So many questions...so little time.

Before you try eliminating ANYTHING, get both equations in the same form (usually Ax + By = C):

2x+ 5y = 6
-3x - 2y = 2 <----I added -6x to both sides of the equation.

It doesn't matter which variable you eliminate....either one is just fine. Note that if we multiply both sides of the first equation by 3, and both sides of the second equation by 2, we can get the coefficients of the x terms to be opposites:

3*2x + 3*5y = 3*6
or,
6x + 15y = 18 <-----new version of first equation

2(-3x) - 2(2y) = 2(2)
or,
-6x - 4y = 4 <-------new version of second equation

Take these new and improved versions of the two equations, and add them together:
6x + 15y = 18
-6x - 4y = 4
---------------
0x + 11y = 22
or,
11y = 22
y = 2

Now, substitute 2 for y in one of the original equations. I'll use the first one:
2x + 5y = 6
2x + 5(2) = 6
2x + 10 = 6
2x = -4
x = -2

Check...are both original equations true when x = -2 and y = 2? I'll let you do the check.

EDITED TO CORRECT STUPID MISTAKE
 
system of linear equations (continued)

According to the back of my book, you are not correct in your outcome. You are partically correct though. I now see where the 6x was eliminated! The -3x -2y = 2 is now multiplied by 5. 5(-3x - 2y) =5(2).Why? This gives you -15x-10y = 10 to go along with the 12 from 4x +10y. So when you add the equation you get -11x = 22 and x = -2. Thanks, for clearning up the Ax +bY =C thing. :)
 
Re: system of linear equations (continued)

marko said:
According to the back of my book, you are not correct in your outcome. You are partically correct though. I now see where the 6x was eliminated! The -3x -2y = 2 is now multiplied by 5. 5(-3x - 2y) =5(2).Why? This gives you -15x-10y = 10 to go along with the 12 from 4x +10y. So when you add the equation you get -11x = 22 and x = -2. Thanks, for clearning up the Ax +bY =C thing. :)

Thank you for pointing out my error.....I fixed it and the solution is now correct. You'll note that I eliminated the x terms in my solution, so you can now see that it is ok to eliminate either of the variables; the solution should be the same.
 
Don't feel bad, Mrspi: 1st mistake this year, right? :wink:
 
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