Question

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

Answer 1

Finding the $x-$coordinate using the substitution method.

Step 1: Finding the value of $y$:

Given equations are:

$\begin{array}{rcl}2x-3y& =& 1...\left(1\right)\\ x+y& =& 3...\left(2\right)\end{array}$

In equation $\left(2\right)$ subtracting $x$ from both sides:

$y=3-x...\left(3\right)$

Step 2: Finding the value of $x$:

Substituting the value of $y$ from equation $\left(3\right)$ in the equation $\left(1\right)$:

$\begin{array}{rcl}2x-3(3-x)& =& 1\\ & \Rightarrow & 2x-9+3x=1\\ & \Rightarrow & 2x+3x=1+9\left[\mathrm{Add}9\mathrm{on}\mathrm{both}\mathrm{sides}\right]\\ & \Rightarrow & 5x=10\\ & \Rightarrow & x=2\left[\mathrm{Divide}\mathrm{by}2\mathrm{on}\mathrm{both}\mathrm{sides}\right]\end{array}$

Therefore, the value of the x- coordinate of the solution of the system $2x-3y=1$ and $x+y=3$ is $2$.