SOLUTION: I am having alot of trouble with these types of questions.. y=7/6x+4 -x+y=1

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Question 571768: I am having alot of trouble with these types of questions..
y=7/6x+4
-x+y=1

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +y+=+%287%2F6%29%2Ax+%2B+4+
(2) +-x+%2B+y+=+1+
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There are different ways to solve
this. Usually, you will be asked
to solve it a certain way.
------------------
First, you must recognize them as
straight line, or linear, equations.
That's because you only see +x+
and +y+, and not +x%5E2+ or +y%5E2+
------------------
Then you should know that there are
2 accepted forms to put them in:
(a)
Standard form:
+ax+%2B+by+=+c+
Point-slope form:
+y+=+mx+%2B+b+
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So, +y+=+%287%2F6%29x+%2B+4+ is in point-slope form
and +-x+%2B+y+=+1+ is in standard form
-------------
Get them both into standard form
(1) +y+=+%287%2F6%29%2Ax+%2B+4+
Multiply both sides by +6+
(1) +6y+=+7x++%2B+24+
Subtract +7x+ from both sides
(1) +-7x+%2B+6y+=+24+
------------------
Now they are both in standard form
Multiply both sides of (2) by 6
and subtract (2) from (1) ( change the signs and add )
(1) +-7x+%2B+6y+=+24+
(2) +6x+-+6y+=+-6+
+-x+=+18+
+x+=+-18+
and, since
(2) +-x+%2B+y+=+1+
(2) +-%28-18%29+%2B+y+=+1+
(2) +18+%2B+y+=+1+
(2) +y+=+-17+
The solution is ( -18, -17 )
check answer:
(1) +y+=+%287%2F6%29%2Ax+%2B+4+
(1) +-17+=+%287%2F6%29%2A%28-18%29+%2B+4+
Multiply both sides by 6
(1) +-102+=+-126+%2B+24+
(1) +-102+=+-102+
OK
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It isn't easy. Do lots of problems and
you'll get better at it.
Here's a plot of the 2 lines. The intersection
is the solution
+graph%28+600%2C+600%2C+-20%2C+4%2C+-20%2C+4%2C+%287%2F6%29%2Ax+%2B+4%2C+x+%2B+1+%29+