Question 1132110
2/x+5/y=5/6; x/2+y/5=5
<pre>{{{matrix(1,3, 2/x + 5/y, "=", 5/6)}}}
12y + 30x = 5xy ------ Multiplying by LCD, 6xy ------ eq (i)

{{{matrix(1,3, x/2 + y/5, "=", 5)}}}
5x + 2y = 50 --------- Multiplying by LCD, 10
5x = 50 - 2y --------- eq (ii)

12y + 30x = 5xy =====> 12y + 6(5x) = y(5x)
12y + 6(50 - 2y) = y(50 - 2y) ------- Substituting 50 - 2y for 5x in eq (i)
{{{matrix(1,3, 12y + 300 - 12y, "=", 50y - 2y^2)}}}
{{{matrix(1,3, 2y^2 - 50y + 300, "=", 0)}}}
{{{matrix(1,3, 2(y^2 - 25y + 150), "=", 2(0))}}}
{{{matrix(1,3, y^2 - 25y + 150, "=", 0)}}}
(y - 15)(y - 10) = 0
y = 15             OR           y = 10

5x = 50 - 2(15) ------- Substituting 15 for y in eq (ii)
5x = 20
{{{matrix(1,5, x, "=", 20/5, "=", 4)}}}
{{{highlight_green(matrix(1,4, Solution, "1:", "(4,", "15)"))}}}

5x = 50 - 2(10) ------- Substituting 10 for y in eq (ii)
5x = 30
{{{matrix(1,5, x, "=", 30/5, "=", 6)}}}
{{{highlight_green(matrix(1,4, Solution, "2:", "(6,", "10)"))}}}</pre>