How do you solve the system 6x^2-5x+8y^2+y=23 and y=x-1?

1 Answer
Ratnaker Mehta
Jul 6, 2016

The Soln. Set ={(2,1), (-4/7,-11/7)}.

Explanation:

We substitute y=x-1.......(I) in the qudr. eqn., to get,

6x^2-5x+8(x-1)^2+x-1=23.
rArr 6x^2-5x+8x^2-16x+8+x-1-23=0.
rArr 14x^2-20x-16=0, or, 7x^2-10x-8=0.
rArr 7x^2-14x+4x-8=0.... ..[7xx8=14xx4, 14-4=10]
rArr 7x(x-2)+4(x-2)=0.
rArr (x-2)(7x+4)=0.
rArr x=2, x=-4/7
(1), thenrArr y=1,y=-11/7

These satisfy the given eqns. Hence,

The Soln. Set ={(2,1), (-4/7,-11/7)}.

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