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Curves: solving
The graphs of

y = ax3+ b
y = mx+ c

cross each other in up to three places.

y = 2x³+1,
y = x		 Number of crossing points: 0123
y = 2x³+1,
y = x+1		 Number of crossing points: 0123
y = 2x³+3,
y = -x+1		 Number of crossing points: 0123
y = 4x³,
y = 5x+1		 Number of crossing points: 0123

What you should understand

A cubic graph and a linear graph will cross eacher other either once only or three times. So the simultaneous equations
y = ax3+ b
y = mx+ c
can have either one answer or three.



a1 a2 a3 a4
b1 b2 b3 b4
c1 c2 c3 c4
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