Given equations can be rearranged as below.

5x +2y =29   ------------(1)

43x + 4y + 2z = 29 -----(2)

67x + 3y + 4z = 29 -----(3)

2 times equation (2) gives 86x + 8y + 4z = 58 ------(4)

equation (4) - equation (3) gives 19x + 5y = 29 --------(5)

5/2 times equation (1) gives 25/2 x + 5y = 29x5/2 ------(6)

equation (5) - equation (6) gives (19-12.5)x = (29-5x29/2) therefore x = -6.69

substitute x value to equation (1) gives y = 31.225 and substitute x value and y value to equation (2) gives z = 95.885

 

When you adding two equations, you have to add left side terms  of each equation together and do the same thing for right side as well. 

 

I think you start with setting each of the equations equal to 29: 5x+2y=29 solve this one for y (in terms of x) 43x+4y+2z=29 67x+3y+4z=29 combine these two so that you eliminate z y= (29-5x)/2 and (86 - 67)x +(8-3)y = 19x+5y = 29. Now you could use these two equations to solve for x and y...but it's faster if you happen to have a graphing calculator. Graph the two lines and find their point of intersection.....(-4.94486, 26.86214) Now just plug these values in and solve for z....I leave that to you.