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}#?

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Answer 1 · 2017-08-15T08:39:05

x = - 3/2 and y = - 4

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#