SOLUTION: Ok, here is the next problem that I am facing. I can figure the first part, but cannot make sense of the second part. 5x+3y=-11 7x-2y=-17 2(5x+3y=-11) = 10x+6y=-33 3(7

Question 244391: Ok, here is the next problem that I am facing. I can figure the first part, but cannot make sense of the second part.
5x+3y=-11
7x-2y=-17
2(5x+3y=-11) =
10x+6y=-33
3(7x-2y=17)=
21x-6y=51
10x+6y=-33
21x+6y=51
31x=18
x=18
31

Correct so far right?
Here is what I can not figure out: I would then take X and substitute into either one of the equations.
I chose the second one.
7(18/31)-2y=17
No logically, I would need to eliminate the y out of the equation somehow, but how?
7(18/31)-2y+2y=17, but then I would have to add it back on behind the 17 right?
Here is what the example from Mathlab shows:
So the only answer that I can derive from this is by multiplying 7(18/31) which equals 126/31, now what??? What do I do with the rest of the equation?
Found 2 solutions by scott8148, edjones:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
5x+3y=-11
7x-2y=-17
2(5x+3y=-11) =
10x+6y=-33 ___ ERROR here ___ -33 should be -22
3(7x-2y=17)=
21x-6y=51 ___ ERROR here ___ 51 should be -51
10x+6y=-33
21x+6y=51
31x=18 ___ 31x = -73
x=18 ___ x = -73/31
31

Correct so far right? ___ NO
Here is what I can not figure out: I would then take X and substitute into either one of the equations.
I chose the second one.

7(18/31) - 2y = 17 ___ 7(-73/31) - 2y = 17
___ 7(-73/31) - 17 = 2y
___ -511/31 - 51/31 = 2y
___ -281/31 = y

No logically, I would need to eliminate the y out of the equation somehow, but how?
7(18/31)-2y+2y=17, but then I would have to add it back on behind the 17 right?
Here is what the example from Mathlab shows:
So the only answer that I can derive from this is by multiplying 7(18/31) which equals 126/31, now what??? What do I do with the rest of the equation?
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
5x+3y=-11
7x-2y=-17
.
10x+6y=-22 not -33
21x-6y=-51 not 51
-----------------add
31x=-73
x=-73/31
.
5(-73/31)+3y=-11 replace x with -73/31
-365/31 +3y=-11
3y=24/31
y=8/31
.
Ed
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