Given
y = x^2 − 9x
3x − y = 7
intersecting points
First solve the second equation for y
y = 3x - 7 .... (1)
Substituting this in the first equation
3x - 7 = x^2 − 9x
x^2 - 12x + 7 = 0
By quadratic formula
x = [12 ± √ ̅(12^2 - 4*7)]/2
= 12 ± √ ̅116)/2
x = 0.6148 or 11.3852
Substituting in (1)
y = 3(0.6148) - 7
= -5.1556
or
y = 3(11.3852) - 7
= 27.1556
So the intersecting points are
(0.6148,-5.1556), (11.3852,27.1556)
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Verified answer
Given
y = x^2 − 9x
3x − y = 7
intersecting points
First solve the second equation for y
y = 3x - 7 .... (1)
Substituting this in the first equation
3x - 7 = x^2 − 9x
x^2 - 12x + 7 = 0
By quadratic formula
x = [12 ± √ ̅(12^2 - 4*7)]/2
= 12 ± √ ̅116)/2
x = 0.6148 or 11.3852
Substituting in (1)
y = 3(0.6148) - 7
= -5.1556
or
y = 3(11.3852) - 7
= 27.1556
So the intersecting points are
(0.6148,-5.1556), (11.3852,27.1556)