Question

Solve the system of equation.

$\begin{array}{l}2x+y=5\\ 4x+y=9\end{array}$

Short answer

The solution is $x=2,y=1$.

Step-by-step solution

Step 1- Consider the equation.

Consider the system of equation

$\begin{array}{l}2x+y=5\left(1\right)\\ 4x+y=9\left(2\right)\end{array}$

Step 2- Step description.

Multiply the equation (1) by 2 such that $4x+2y=10$. (3)

Subtract the equation (2) from the equation (3) as follows:

$\begin{array}{l}4x+2y-(4x+y)=10-9\\ 4x+2y-4x-y=1\\ y=1\end{array}$

Step 3- Step description.

Substitute the value of y in equation (1).

$\begin{array}{l}2x+y=5\\ 2x+1=5\\ 2x=4\\ x=2\end{array}$

Therefore, the solution is $x=2,y=1$.