The sum of two numbers is 62 and their product is 960 the sum of their reciprocals is

x =  first number, y = second number

difference is 10, means       y-x = 10

You can solve a system of equations by Substitution, Elimination, Graphing, or Matrices.

Graphing is probably not the best for this one, but it is possible by putting both equations in y=mx+b form and putting into a graphing calculator.

Now substitute for x in the second equation

Now substitute y into original equation (either will work)

-x +y = 10       Now add the two equations together

substitute y into either equation as in substitution (either works)

Put the Coefficients and constants into a matrix as follows:

either multiply a row by a number or add a row by the other row multiplied by a number.

Get the matrix in the form

Easier to start with the a 0, so get the -1 in the second row to 0

[-1+(1*1)  1+(1*1) | 10+(1*62) ]

[ 0*(1/2) 2*1/2) | 72*(1/2)]

[ 0 1 | 36 ]  <-- we now have the y value

[ 1+(-1*0) 1+(-1*1) | 62+(-1*36) ]

[ 1 0 | 26 ]  <-- we now have x value

[ 0 1 | 36 ]  <-- and we have y value