How do you solve this system of equations: #y= - 2x ^ { 2} + 28x - 75 ; 3= 2x - y#?

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Answer 1 · 2018-04-26T17:42:16

#"The Solution Set is "{(9,15), (4,5)}#.

Given the eqns.

# (1) : y=-2x^2+28x-75, and, (2) : 3=2x-y#.

From #(2), y=2x-3#.

Sub.ing in #(1), 2x-3=-2x^2+28x-75, or, #

# 2x^2-26x+72=0#.

#:. x^2-13x+36=0#.

# :. (x-9)(x-4)=0#.

#:. x=9, or, x=4#.

Then, #y=2x-3 rArr x=9, then, y=2xx9-3=15, or, #

#"for "x=4, y=8-3=5#.

#:. (x,y)=(9,15), or, (4,5)#.

These roots also satisfy #(1) and (2)#.

Thus, #"The Solution Set is "{(9,15), (4,5)}#.