SOLUTION: for what values of k does the system of equations y=x^2-3x+5 , y=kx have only 1 solution? leave your answers in exact form. Please help me with this question or atleast give me a

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Question 933103: for what values of k does the system of equations y=x^2-3x+5 , y=kx
have only 1 solution? leave your answers in exact form.
Please help me with this question or atleast give me a hint.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
kx=x%5E2-3x%2B5 by substitution.
x%5E2-3x%2B5-kx=0
x%5E2-3x-kx%2B5=0
x%5E2-%283%2Bk%29x%2B5=0

The expression for that equation's discriminant is %283%2Bk%29%5E2-4%2A1%2A5.
Discriminant value of 0 means the quadratic equation x%5E2-%283%2Bk%29x%2B5=0 is a perfect square on the left side member, the quadratic expression.

%283%2Bk%29%5E2-20=0
k%5E2%2B6k%2B9-20=0
k%5E2%2B6k-11=0
k=%28-6%2B-+sqrt%2836%2B44%29%29%2F2
k=%28-6%2B-+sqrt%2880%29%29%2F2
k=%28-6%2B-+4%2Asqrt%285%29%29%2F2
highlight%28k=-3%2B-+2sqrt%285%29%29, either of these two values for k so that the two given equations meet in exactly one point.