Question

How do you solve this system of equations : `\frac { 1} { 3} x - \frac { 1} { 2} y = 1;\frac { 1} { 2} x - \frac { 1} { 4} y = - \frac { 1} { 2}`?

Answer 1

x = - 3/2 and y = - 4

Explanation:

Here, Say `x/3-y/2 = 1 ............. (i)` &
`x/2-y/4 = -1/2 .................. (ii)`

Now multiply equation (i) by 1/2 and eqn (ii) by 1/3. we get -

`x/6-y/4 = 1/2 ..... (iii)` &
`x/6-y/12 = -1/6 ..... (iv)`

Now subtract (iv) from (iii), we get -

`-y/4+y/12 = 1/2+1/6`

or, `y = -4`

put the value of y = -4 in eqn(ii), we get

`x/2 -(-4)/4`= -1/2

or, `x/2 + 1 = -1/2`

or, `x = -1/2 -1 =-3/2`