Question

Simultaneous linear equations
Solve
3/2x +2/3y =-1/3 and 3/4x + 1/2y =-1/8

Answer 1

3/2x+2/3y=-1/3 -----------(1)
3/4x+1/2y=-1/8 -----------(2)
Multiplying (1) with (1/2) and (2) with 1 and subtracting we get,
3/4x+1/3y=-1/6
3/4x+1/2y=-1/8
1/3y-1/2y=-1/6+1/8
or, (2-3)/6y=(-4+3)/24
or, -1/6y=-1/24
or, 1/y=1/4
or, y=4
3/2x=-1/3-2/12
or, 3/2x=-1/3-1/6
or, 3/2x=(-2-1)/6
or, 3/2x=-3/6
or, 1/x=-1/2×2/3
or, 1/x=-1/3
or, x=-3
x=-3, y=4

Answer 2

3/2x +2/3y =-1/3 and 3/4x + 1/2y =-1/8

$\frac{3}{2}x+\frac{2}{3}y=-\frac{1}{3}---(1)\\\\\frac{3}{4}x+\frac{1}{2}y=-\frac{1}{8}---(2)\\\\Multiply, \ (2)\ with\ 2\ and\ subtract\ from\ (1):\\\\(\frac{2}{3}-2*\frac{1}{2})y=-\frac{1}{3}+2*\frac{1}{8}\\\\-\frac{1}{3}y=-\frac{1}{12}\\\\y=\frac{1}{4}\\\\\frac{3}{2}x=-\frac{1}{3}-\frac{2}{3}*\frac{1}{4}\ from\ (1)\\\\x=-\frac{1}{3}$