Solve the simultaneous equations 3x -y=5, 4x -3y=-1. Hence, find p, if y=px-3
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This question requires that you find the values of p and r, which i assume before solving, are equal.
Now, if x-3 and x-1/3 are both factors to this expression , it means their division gives a value of zero.
Now lets use x-3
>>> let x-3=0.
>>> x=3
Now substitute x=3 into the expression
>>>> Px^2+3x+r
>>> P (3)^2 + 3(3) +r = 0
>>> 9p+ r + 9= 0
>>> 9p+r= -9 ……..(1) simultaneous eqn
Now use x-1/3.
Let x-1/3=0
>>> x=1/3
Now substitute x=1/3 into the polynomial
>>> P(1/3)^2+ 3(1/3) + r=0
>>> P(1/9)+ 1 +r =0
>>> P(1/9) + r= -1
>>> P + 9r = -9…(2) simultaneous eqn
Subtract (1) from (2)
>>> 9p+ r =-9
-
P + 9r =-9
>>> 8p - 8r = 0
>>> 8p = 8r
>>> p = r
As required.
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