Question

Y=x+1
y=x^2-1

please help i don't understand

Answer 1

The solution is

`(x=1,y=2),(x=2,y=3)`

Step-by-step explanation

We have

`y=x+1---(1)`

and

`y=x^2-1---(2)`

Let us substitute equation (1) in to equation (2). This gives us,

`x+1=x^2-1(2)`

We rewrite this as a quadratic equation as the highest degree is 2.

`x^2-x-1-1=0`

This implies that

`x^2-x-2=0`

we factor to obtain,

`x^2+x-2x-2=0`

`x(x-1)-2(x-1)=0`

`(x-1)(x-2)=0`

This means,

`(x-1)=0\:\: or\:\:(x-2)=0`

`x=1\:\: or\:\:x=2`

We substitute this values into any of the above equations, preferably equation (1)

When,
`x=1`,
`y=1+1=2`

When,
`x=2`,
`y=2+1=3`

The solution is

`(1,2),(2,3)`