Question

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

Answer 1

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)`, then`rArr y=1,y=-11/7`

These satisfy the given eqns. Hence,

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