SOLUTION: How do I graph and determine the solution set of: x=7-2y y=3x What i tried to do was set them to zero, but I didn't know what else to do..please help!

Algebra ->  Graphs -> SOLUTION: How do I graph and determine the solution set of: x=7-2y y=3x What i tried to do was set them to zero, but I didn't know what else to do..please help!      Log On


   



Question 577267: How do I graph and determine the solution set of:
x=7-2y
y=3x
What i tried to do was set them to zero, but I didn't know what else to do..please help!

Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do I graph and determine the solution set of:
x=7-2y
Solve for "y":
2y = -x+7
y = (-1/2)x+(7/2)
Plot 2 points:
If x = 2, y = -1+(7/2) = 2 1/2
If x = 0, y = (7/2) = 3 1/2
---
Plot (2,2 1/2) and (0, 3 1/2) and draw a line thru them.
=================
y=3x
If x = 0, y = 0
If x = 1, y = 3
=================
Plot (0,0) and (1,3) and draw a line thru them.
----
Find the point of intersection of the 2 lines.
That is the solution of the set of 2 solutions.
===============
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C3x%2C%28-x%2B7%29%2F2%29
===============
Cheers,
Stan H.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
These are 2 straight lines and the solution
is their intersection. Since 2 straight lines
can only intersect at 1 point, there is only
1 solution.
------------
Get both lines into the standard form:
(1) +x+=+7+-+2y+
(1) +x+%2B+2y+=+7+
and
(2) +y+=+3x+
(2) +3x+-+y+=+0+
----------------
Now multiply both sides of (2) by +2+,
and add the equations
(1) +x+%2B+2y+=+7+
(2) +6x+-2y+=+0+
+7x+=+7+
+x+=+1+
Now plug this value back into either (1) or (2)
(2) +3%2A1+-+y+=+0+
(2) +-y+=+-3+
(2) +y+=+3+
The solution is (1,3)
Here's a plot of the lines:
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+3x%2C+-%281%2F2%29%2Ax+%2B+7%2F2+%29+