# solving a system of 2 equations with 2 variables

write equation for sum of reciprocals

One number is 2 times another.

Write an expression for the sum of their reciprocals.

Simplify the expression. (Use x for the variable.)

### Comments for solving a system of 2 equations with 2 variables

 May 05, 2014 sum of reciprocals by: Staff Answer Part I x = 1st number z = 2nd number y = sum of the reciprocals y = (1/x) + (1/z) z = 2x substitute 2x for z y = (1/x) + (1/(2x)) --------------------------------------------

 May 05, 2014 sum of reciprocals by: Staff -------------------------------------------- Part II multiply each side of the equation by 2x 2x * y = 2x * [(1/x) + (1/(2x))] Expand using the distributive law 2x * y = 2x * [(1/x) + (1/(2x))] 2xy = (2x / x) + (2x / (2x)) Simplify the right side of the equation by cancelling like terms 2xy = 2 + 1 2xy = 3 --------------------------------------------

 May 05, 2014 sum of reciprocals by: Staff -------------------------------------------- Part III Divide by 2x 2xy / (2x) = 3 / (2x) y = 3 / (2x) y = 1.5 / x the final answer is: y = 1.5 / x, x ≠ 0 --------------------------------------------

 May 05, 2014 sum of reciprocals by: Staff -------------------------------------------- Part IV Thanks for writing. Staff www.solving-math-problems.com