$\"\"$

Write a system of equations:

Let the two numbers are $\"\"$ .

The sum of these two numbers is 22 then the equation $\"\"$ .

The difference of these two numbers is 12 then the equation $\"\"$ .

Elimination method:

The system of equations are

$\"\"$ ----------(1)

$\"\"$ ----------(2)

In the above system the coefficients of y - variable are opposite. $\"\"$

Add the equations to eliminate the y - variable and solve the equation.

$\"\"$

The resultant equation is $\"\"$ .

Divide each side by 2.

$\"\"$

The value of $\"\"$ substitute in either equation to find y.

First equation: $\"\"$ .

$\"\"$

Subtract 17 from each side.

$\"\"$

The solution is $\"\"$ .