Question

x+y=18
1/x+1/y=1/4
solve this question plz​

Answer 1

Answer:

Find a common denominator for 1/x and 1/y.

1/x=y/xy. 1/y=x/xy

y/xy + x/xy =1/4 by substitution

(y + x)/xy =1/4

(x + y)/xy=1/4 since addition is commutative.

4(x + y)/xy =1 since 1/4 times 4 equals 1.

4(x + y)=xy since multiplying both sides by xy

4x + 4y=xy by distributive property of multiplication over addition.

4x -xy + 4y=0

This requires factorization.

I’m getting nowhere with this. I am sure that x=8 and y=8 work because 1/8+ 1/8=1/4 but this is only from observation not “solving “ the equation.

4/16=1/4 but 3/16 + 1/16 has a different numerator from the equation we are asked to solve!