Question

Where do the lines given by y=x+b and y=2x+1 intersect?

Answer 1

`x=b-1\\y=2b-1`

Explanation:

We have a 2x2 equation system. First, rewrite it like this:

`-2x+y=1\hspace{5}(1)\\-x+y=b\hspace{5}(1)`

Solving the system using elimination method:

(1)-(2)

`-2x-(-x)+y-y=1-b\\x=b-1\hspace{5}(3)`

Replacing (3) in (2)

`-(b-1)+y=b\\`

Adding (b-1) to both sides:

`y=b+(b-1)=b+b-1=2b-1`