Solving Simultaneous Equations:

The easiest system of equations is one including two linear equations along with two unknowns.

5x + 6y            = 12

3x + 5y            = 3

The approach used to solve systems of two linear equations including two unknowns is to combine the two equations in such a way in which one of the unknowns is eliminated.  The output equation can be solved for one unknown, & either of the original equations can then be used to solve for the other unknown.

Systems of two equations involving two unknowns can be solved by addition or subtraction using five steps.

Step 1. Multiply or divide one or both equations by some factor or factors which will make the coefficients of one unknown numerically equal in both equations.

Step 2. Eliminate   the   unknown   having   equivalent   coefficients   through   addition   or subtraction.

Step 3. Solve the resulting equation for the value of the one remaining unknown.

Step 4. Find out the value of the other unknown through substituting the value of the first unknown within one of the original equations.

Step 5. Check the solution by substituting the values of the two unknowns within the other original equation.