SOLUTION: Where does the equations y=-6x+30 and y=3x-6 intersect? I need the solution. Please HELP ME RIGHT AWAY!

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Question 658968: Where does the equations y=-6x+30 and y=3x-6 intersect? I need the solution. Please HELP ME RIGHT AWAY!
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Where does the equations y=-6x+30 and y=3x-6 intersect?
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Actually, the lines of the graphs intersect, not the equations themselves.
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y=-6x+30 and y=3x-6
Since they both equal y:
-6x+30 = 3x-6
30 = 9x-6
36 = 9x
x = 4
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y = 3x-6
y = 6
Intersection at (4,6)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Hi
These equations are in the slope-intercept form.
I would put them into the standard form which
looks like +ax+%2B+by+=+c+
+y+=+-6x+%2B+30+
Add +6x+ to both sides
(1) +6x+%2B+y+=+30+
and
+y=3x-6+
Subtract +y+ from both sides
+0+=+3x+-+y+-+6+
Add +6+ to both sides
+6+=+3x+-+y+
Now write it the other way around
(2) +3x+-+y+=+6+
Add equations (1) and (2)
(1) +6x+%2B+y+=+30+
(2) +3x+-+y+=+6+
+9x+=+36+
+x+=+4+
Now plug this result back into (1) or (2)
(1) +6%2A4+%2B+y+=+30+
(1) +24+%2B+y+=+30+
(1) +y+=+30+-+24+
(1) +y+=+6+
The intersection is at ( 4,6 )
Here's the plot:
+graph%28+400%2C+400%2C+-4%2C+10%2C+-4%2C+10%2C+-6x+%2B+30%2C+3x+-+6+%29+