Question 201190
A,{Y=^X2+4X-5 & Y=-X^2+12X-11
I assume you want to find the values of x common to these 2 eqns, where they intersect.
Since they both = y, they equal each other.
X^2+4X-5 = -X^2+12X-11
2x^2 - 8x + 6 = 0
(2x - 2)*(x - 3) = 0
x = 3
x = 1
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x = 3 --> y = 16 gives the point (3,16)
x = 1 --> y = 0 gives the point (1,0)
These are the 2 points of intersection of the 2 functions.
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B, X^2+Y^2=193 &X-Y=5
x = y+5
(y+5)^2 + y^2 = 193
y^2 + 10y + 25 + y^2 = 193
2y^2 + 10y - 168 = 0
y^2 - 5y - 84 = 0
(y-12)*(y+7) = 0
y = -7
y = 12
Sub and solve for x as in the 1st one.
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C X*Y=45 & 3X-Y=-6
y = 3x+6
x*(3x+6) = 45
x^2 + 2x - 15 = 0
(x+5)*(x-3) = 0
x = 3
x = -5
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D X*Y=8 & X^2+Y^2=65
Similar to B but with 4 points of intersection.
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E X+Y=-8 & (X-2)^2+(Y+7)^2=5
More of the same
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