SOLUTION: What is the answer to x=y-7 2x-5y=-2 AND I also need to know -3x+2y=10 -2x-y=-5

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Question 171950: What is the answer to
x=y-7
2x-5y=-2
AND I also need to know
-3x+2y=10
-2x-y=-5
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
x=y-7, EQN 1 -------> y=x%2B7
2x-5y=-2, EQN 2 -----> %282x%2B2%29%2F5=y
Subst. EQN 1 in EQN 2:
2%28y-7%29-5y=-2
2y-14-5y=-2
-3y=-2%2B14=12 -------->cross%28-3%29y%2Fcross%28-3%29=cross%2812%294%2Fcross%28-3%291
highlight%28y=-4%29
subst. in EQN 1:
x=-4-7=highlight%28-11%29
The lines intersect thru these points(-11,-4) as shown:
---> RED Line, EQN 1; GREEN Line, EQN 2
.
-3x%2B2y=10, EQN 3 -------> y=%283x%2B10%29%2F2=%283%2F2%29x%2B%2810%2F2%29
-2x-y=-5, EQN 4 --------> y=-2x%2B5
We equate the 2 eqn's:
-2x%2B5=%283%2F2%29x%2B5
%283%2F2%29x%2B2x=5-5
%283%2B6%29x%2F2=0 -->highlight%28x=0%29
Subst x=0 in EQN 4:
-2%280%29-y=-5 ------> highlight%28y=5%29
Therefore, these lines intersect at points(0,5), as we see:

-----> RED Line, EQN 3; GREEN Line, EQN 4
Thank you,
Jojo