Question 4561
6x + 4y =8
9x + 6y =12

Multiply the second equation by 2/3:
6x + 4y = 8
6x + 4y = 8

These are identical so they are the same line!

Second problem:

{{{2x/3 + 3y/4 =4}}}
{{{5x/6 - 3y/8 = -11/2}}}

Since I don't want to work with fractions, I will:
Multiply the first equation by 12 to clear the denominators
Multiply the second equation by 24 to clear the denominators

8x + 9Y = 48
20x- 9y = -132

Add them together:
28x = -84
Divide both sides by 28:
x=3

substitute back into either equation:
{{{2(3)/3 + 3y/4 =4}}}

Clear parentheses:
{{{2+ 3y/4 = 4}}}

subtract 2 from each side:
{{{3y/4 = 2}}}


Multiply both sides by 4/3:
{{{y=8/3}}}


check by putting x and y back into the second equation to validate:

{{{5x/6 - 3y/8 = -11/2}}}
{{{5(3)/6-(3/8)*(8/3)=-11/2}}}
{{{5/2-1=-11/2}}}
{{{5/2-2/2=-11/2}}} 
this is not a true statement, so this problem has no solution.