Question

How do you solve system of equations `y = x+1` and `y = 2x -1`?

Answer 1

x=2; y=3

Substitute y= x+1 from the first equation into the second equation. it would become x+1= 2x-1. Now add 1 on both sides and also subtract x from both sides. It would become 2=x. that is x=2. Now in the 1st equation, plugin x=2, to get y= 2+1 =3.

Answer 2

`y = x + 1` ...equation 1
`y = 2x - 1` ...equation 2

subtract equation 1 from equation 2.

equation 2 - equation 1
`=> y - y = [2x - 1] - [x + 1]`

`=> 0 = 2x - x - 1 -1`

`=> 0 = x - 2`
`x - 2 = 0` Right ?!

`=> x = 2`

put `x = 2` in equation 1 OR 2

in equation 1:
`y = x + 1`
`=> y = 2 + 1`
`=> y = 3`

OR
in equation 2:
`y = 2x - 1`
`=> y = 2*(2) - 1`
`y = 4 - 1`
`=> y = 3` As above for equation 1

Hence `x = 2` and `y = 3`