SOLUTION: i know how to do linear combination, but i cannot get the right answer for this problem: 2x+y+52=2y+50 2x+y+52=x-3y+131 I need help finding x and y. Thank you!

Question 103732: i know how to do linear combination, but i cannot get the right answer for this problem:
2x+y+52=2y+50
2x+y+52=x-3y+131
I need help finding x and y.
Thank you!
Found 2 solutions by stanbon, oberobic:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
2x+y+52=2y+50
2x+y+52=x-3y+131
-------------
Simplify each equation:
1st: 2x -y = -2
2nd: x +4y = 79
------------------
Multiply 1st thru by 4 to get:
3rd: 8x -4y = -8
----------------
Add 2nd and 3rd to solve for x:
9x =71
x = 71/9
--------------------
Substitute into 2x-y = -2 to solve for y:
2(71/9) - y = -2
y = 142/9+18/9
y = 160/9
----------------
Checking in 2nd:
71/9 + 4(160/9) = 79
(71 + 640)/9 = 79
711/9 = 79
79 = 79
===============
Cheers,
Stan H.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
First, always look at what you've been given
Equation 1: 2x+y+52=2y+50
Equation 2: 2x+y+52=x-3y+131
So, the transitive property tells us:
2y +50 = x -3y + 131
Subtracting 2y from both sides:
50 = x -3y + 2y + 131
Subtracting 50 from both sides:
0 = x -3y + 2y + 131 -50
Combining:
0 = x + y + 81
Subtracting x from both sides:
-x = y + 81
Multiplying by -1:
x = -y -81
Now you can substitute into Eq 1:
2(-y -81) +y +52 = 2y + 50
-2y -162 +y + 52 = 2y + 50
Combining:
-y -110 = 2y + 50
Adding y to both sides:
-110 = 3y + 50
Subtracting 50 from both sides:
-160 = 3y
Dividing through by 3:
-(53+1/3) = y
Since x+y+81=0, then
x+(-(53+1/3))+81=0
x+(27+2/3)=0
Subtract 27 2/3 from both sides
x = -27 2/3
ALWAYS check your work!
x+y=-81
-(27+2/3)+(-(53+1/3))-81 = 0. True
2x+y+52=2y+50
Lefthand side=
2*(-(27+2/3))+(-(53+1/3))+52=-56 2/3
Righthand side=
2(-(53+1/3))+50=-56 2/3
True again.

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