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

Mar 29, 2015

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.

Mar 29, 2015

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

subtract equation 1 from equation 2.

equation 2 - equation 1
$\implies y - y = \left[2 x - 1\right] - \left[x + 1\right]$

$\implies 0 = 2 x - x - 1 - 1$

$\implies 0 = x - 2$
$x - 2 = 0$ Right ?!

$\implies x = 2$

put $x = 2$ in equation 1 OR 2

in equation 1:
$y = x + 1$
$\implies y = 2 + 1$
$\implies y = 3$

OR
in equation 2:
$y = 2 x - 1$
$\implies y = 2 \cdot \left(2\right) - 1$
$y = 4 - 1$
$\implies y = 3$ As above for equation 1

Hence $x = 2$ and $y = 3$