Question

Solve the system of equation.

$\begin{array}{l}x+y=10\\ 2x+y=11\end{array}$

Short answer

The solution is $x=1,y=9$.

Step-by-step solution

Step 1- Consider the equation.

Consider the system of equation

$\begin{array}{l}x+y=10\left(1\right)\\ 2x+y=11\left(2\right)\end{array}$

Step 2- Step description.

Multiply the equation (1) by 2 such that $2x+2y=20$. (3)

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

$\begin{array}{l}2x+2y-(2x+y)=20-11\\ 2x+2y-2x-y=20-11\\ y=9\end{array}$

Step 3- Step description.

Substitute the value of y in equation (1).

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

Therefore, the solution is $x=1,y=9$.