Question

Solve the system of equation.

$\begin{array}{l}6x+2y=22\\ 3x+7y=41\end{array}$

Short answer

The solution is $x=2,y=5$.

Step-by-step solution

Step 1- Consider the equation.

Consider the system of equation

$\begin{array}{l}6x+2y=22\left(1\right)\\ 3x+7y=41\left(2\right)\end{array}$

Step 2- Step description.

Multiply the equation (2) by 2 such that $6x+14y=82$. (3)

Subtract the equation (1) from the equation (3) as follows:

$\begin{array}{l}6x+14y-(6x+2y)=82-22\\ 6x+14y-6x-2y=60\\ 12y=60\\ y=5\end{array}$

Step 3- Step description.

Substitute the value of x in equation (1).

$\begin{array}{l}6x+2y=22\\ 6x+2\left(5\right)=22\\ 6x+10=22\\ 6x=12\\ x=2\end{array}$

Therefore, the solution is $x=2,y=5$.