SOLUTION: 2x + 2y=8 and 4x-6y=36 solution (6,2) how did my text book come up with thesesolutions

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Question 187419: 2x + 2y=8 and 4x-6y=36

solution (6,2) how did my text book come up with thesesolutions

Found 2 solutions by nerdybill, josmiceli:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming you are expected to solve a system linear equations using the "elimination method":
.
2x + 2y = 8
4x - 6y = 36
.
multiply both sides of the top equation and add it to the second:
6x + 6y = 24
4x - 6y = 36
------------
10x = 60
Dividing both sides by 10:
x = 6
.
Now, we plug the value above into either equation to find y. Let's pick the top one:
2x + 2y = 8
2(6) + 2y = 8
12 + 2y = 8
2y = -4
y = -2
.
therefore:
(x,y) = (6, -2)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) 2x+%2B+2y+=+8
Divide both sides by 2
(1) x+%2B+y+=+4
(1) x+=+4+-+y
(2) 4x+-+6y+=+36
Divide both sides by 2
(2) 2x+-+3y+=+18
Substitute (1) in (2)
(2) 2%2A%284+-+y%29+-+3y+=+18
(2) 8+-+2y+-+3y+=+18
(2) -5y+=+10
(2) y+=+-2
Substitute this back into (1)
(1) x+=+4+-+y
(1) x+=+4+-+%28-2%29
(1) x+=+4+%2B+2
(1) x+=+6
The answer is (6,-2)
check answer:
(1) 2x+%2B+2y+=+8
(1) 2%2A6+%2B+2%2A%28-2%29+=+8
(1) 12+-+4+=+8
8+=+8
(2) 4x+-+6y+=+36
(2) 4%2A6+-+6%2A%28-2%29+=+36
(2) 24+%2B+12+=+36
(2) 36+=+36
OK