Question

Solve the system of equations.
$$\begin{gathered} 2x+y=3 \\ x=2y-1 \end{gathered}$$

Answer 1

Determine the values of $x,y$ from the given equations:

The given equations are as :

$$\begin{gathered} 2x+y=3 \\ x=2y-1 \end{gathered}$$

Using the Substitution method, to substitute the value of one of the variables into another equation to get the required results.

Substitute the value of $x=2y-1$ in the given equation $2x+y=3$:

$\begin{array}{rcl}& \Rightarrow & 2\left(2y-1\right)+y=3\\ & \Rightarrow & 4y-2+y=3\\ & \Rightarrow & 4y+y=3+2\\ & \Rightarrow & 5y=5\\ & \Rightarrow & y=1\end{array}$

Substitute the value of $y=1$ in an equation to evaluate the value of $x$ as:

$$\begin{gathered} \Rightarrow x=2y-1 \\ \Rightarrow x=2-1 \\ \Rightarrow x=1. \end{gathered}$$

Therefore, the solution of the system of equation is $x=1,y=1$.