SOLUTION: I am working on systems of Linear Equations, solving using the addition method If it is inconsistent we are to state such, if it is dependent we indicate, x, and answer. I know t

Question 604408: I am working on systems of Linear Equations, solving using the addition method
If it is inconsistent we are to state such, if it is dependent we indicate, x, and answer.
I know this should be simple, I cannot get the hang of it, I tried to follow the book, to no avail.

{ x-7 + y + 9 = 5
--- ----
5 2

x+9 + y-7 = 6
___ ___
2 3
2(x-7) + 5(y+9) = 50
3(x+9) + 2(y-7) = 36
2x + 5y = 19
3x + 2y = 23
5x + 7y = 42
x = 7y + 42 / 5

I really dont know what I am doing or what I should do at this point. I would deeply appreciate assistance. Thank you!

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

In the first equation the LCD = 10.
Multiply equation by 10
2(x-7)+5(y+9)=50
2x-14+5y+45=50
2x+5y=19................(1)

LCD = 6. Multiply equation by 6
3(x+9)+2(y-7)=36
3x+27+2y-14=36
3x+2y=23.......................(2)
Solve (1) & (2)
multiply (1)by -2
Multiply (2) by 5
-4 x -10 y = -38
15 x + 10 y = 115
Add the two equations
11 x = 77
/ 11
x = 7.00
plug value of x in (1)
2 x + 5 y = 19
14.00 + 5 y = 19
5 y = 19 -14.00
5 y = 5
y = 1.00
The rest of them are similar
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