The sum of four times a number and six times a second number is .

Let be a first number and be a second number.

Hence the equation is .

The difference of five times the second number and three times of a first number is .

Hence the equation is .

The system of equations are and .

Solve the system of equations by elimination method.

Step 1:

Multiply each equation with a suitable multiplier.

Case (i):

                      (First equation)

            (Multiply each side by )

               (Multiply)

Case (ii):

                   (Second equation)

         (Multiply each side by )

            (Multiply)

Step 2:

Add the equations to eliminate the one variable.

                    (Divide each side by )

                                  (Cancel common terms)

Step 3:

Substitute into any original equation to find value.

                     (Second equation)

                  (Substitute )

                    (Multiply)

(Subtract from each side)

                           (Apply additive inverse property: )

                   (Divide each side by )

                             (Cancel common terms)

Therefore, the solution is .

The solution of the system is .