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

Aug 3, 2015

$\textcolor{red}{x = 2 , y = 3}$

#### Explanation:

One way is to use the method of substitution.

Step 1. Enter the equations.

[1] $y = x + 1$
[2] $y = 2 x - 1$

Step 2. Substitute the value of $y$ from Equation 1 into Equation 2.

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

[3] $x = 2$

Step 3. Substitute Equation 3 into Equation 1.

$y = x + 1$
$y = 2 + 1$

$y = 3$

Solution: $x = 2 , y = 3$

Check: Substitute the values of $x$ and $y$ in Equations 1 and2.

(a) In Equation 1

$y = x + 1$
$3 = 2 + 1$
$3 = 3$

(b) In Equation 2

$y = 2 x - 1$
$3 = 2 \left(2\right) - 1$
$3 = 4 - 1$
$3 = 3$

It checks!

Our solution is correct.