Question

Y=x+1 y=x^2-1 please help i don't understand

Answer 1

ANSWER

The solution is

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

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

$(1,2),(2,3)$