Question 45903
Lets day the equations are numbered 1, 2 & 3 as under

3x - 4y = -3  ....... 1
6x + 2z = -7/2 ...... 2
2y - 4z =  4   ...... 3

The approach is to use one equation to express the value of one of the variables in terms of the other, and then use this value in another equation, as a result of which we get 2 equations in 2 variables, which can then be easily solved. Note -

Eq 3 is divided by 2 to give :

y - 2z = 2 ;

So we may write

y = 2 - 2z ....  4

Use this value of y in eq 1 above, we get

3x - 4(2-2z) = -3

or 

3x - 8 + 8z = -3
or

3x + 8z = 5 ...... eq no 5

Multiply this equation by 2, we get

6x + 16z = 10 .... eq no 6

Subtract eq no 2 from eq no 6, we get

6x + 16z - 6x - 2z = 10 + 7/2
or
14z = 10 + 7/2
or 
z = 10/14 + 7/(2*14)

or 
z = 5/7 + 1/4 =27/28. 

Use this value of z in eq 2 to get the value of x & eq 3 to get the value of y.