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

Mar 4, 2017

See the entire solution process below:

#### Explanation:

Step 1) Because the first equation is already solve for $y$, substitute $x + 1$ for $y$ in the second equation and solve for $x$:

$y = 2 x - 1$ becomes:

$x + 1 = 2 x - 1$

$x + 1 - \textcolor{red}{x} + \textcolor{b l u e}{1} = 2 x - 1 - \textcolor{red}{x} + \textcolor{b l u e}{1}$

$x - \textcolor{red}{x} + 1 + \textcolor{b l u e}{1} = 2 x - \textcolor{red}{x} - 1 + \textcolor{b l u e}{1}$

$0 + 2 = x - 0$

$2 = x$

$x = 2$

Step 2) Substitute $2$ for $x$ in the first equation and calculate $y$:

$y = x + 1$ becomes:

$y = 2 + 1$

$y = 3$

The solution is: $x = 2$ and $y = 3$ or $\left(2 , 3\right)$