# What is the x-coordinate of the solution of the system 2x-3y=1 and x+y=3?

Apr 8, 2015

The two equations given to us are:
$2 x - 3 y = 1$ -----(1)
$x + y = 3$ -----(2)

To find $x$, we can use the Elimination by Substitution Method
All we need to do is substitute the value of $y$ from (2) in (1)
The second equation is:
$x + y = 3$
Transposing $x$ to the other side, we get:
$y = 3 - x$

Now we simply substitute this value of $y$ in (1)
$2 x - 3 \left(3 - x\right) = 1$

$2 x - 9 + 3 x = 1$

$2 x + 3 x = 1 + 9$

$5 x = 10$

Dividing both sides by 5, we get:

$\frac{\cancel{5} x}{\cancel{5}} = \frac{10}{5}$

color(green)(x = 2

The x-coordinate of the solution of the system 2x−3y=1 and x+y=3 is color(green)(2