Twise the sum of a number and times a second number is .

Let be a first number and be a second number.

Hence the equation is .

The difference of ten times the second number and five times the 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.

                   (First equation)

               (Divide each side by )

                         (Cancel common terms)

               (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 of the system is .

The solution of the system is .