SOLUTION: Graph the system of equations y=x^4-3x³ and y=2x-6. Find the points of intersection. Give an exact answer. PLEASE HELP ME! I don't know what to do!!

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Question 166393: Graph the system of equations y=x^4-3x³ and y=2x-6. Find the points of intersection. Give an exact answer. PLEASE HELP ME! I don't know what to do!!
Found 2 solutions by jojo14344, Fombitz:
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
system of equations y=x%5E4-3x%B3---> EQN 1, and y=2x-6----> EQN 2:
EQN 1:
If you look on the graph below, we find highlight%28x=1.25%29 closest,so
y=%281.25%29%5E4-3%281.25%29%5E3=2.44-5.859
highlight%28y=-3.418%29
EQN 2:
f(y)=0: 2x=6 --->cross%282%29x%2Fcross%282%29=cross%286%293%2Fcross%282%29
x=3
f(x)=0: y=-6
SEE GRAPH:
--- See points of intersection-->(3,0) & (1.25,-3.418)
Thank you,
Jojo

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
+graph%28+300%2C+300%2C+-5%2C+5%2C+-10%2C+10%2C+2x-6%2C+x%5E4-3x%5E3%29+
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A closer look
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+graph%28+300%2C+300%2C+-1%2C+5%2C+-5%2C+5%2C+2x-6%2C+x%5E4-3x%5E3%29+
Looks like (3,0) may be an intersection point.
Try it.
y=2x-6
0=2(3)-6
0=0
True.
y=x^4-3x^3
0=3^4-3(3^3)
0=0
True
(3,0) is a solution.
+graph%28+300%2C+300%2C+-1%2C+3%2C+-5%2C+1%2C+2x-6%2C+x%5E4-3x%5E3%29+
Can't find the second solution exactly by graphing.
Iteration is required.
x=1.25 is a good start point.
Iteration leads to x=1.259922 with corresponding y=-3.48016.