The left-hand side you build by making a matrix with three rows and one column: click Matrices/Tables|Insert Matrix in the top menu, then drag the cursor over the grid of boxes until you have specified the correct dimensions.

Next, enter each equation, one in each placeholder box in the new matrix. The = symbol is made by doing [Ctrl]-[=].

To make the arrow with solve, click Math|Symbolics in the top menu, then click on the right arrow symbol. Next, type solve,x,y,z into the placeholder box above the arrow. When you hit the Enter key on your keyboard, you will get the result. When I tried this example in Prime 5, my result was not as compact as yours (my first result was 11*a/38+7*b/38+c/38). I added the simplify keyword to the arrow but it didn't do anything.

One other thing, for consistency and good document management, I suggest using the multiplication symbol between the coefficients and the variables. In your example, only 4*x in the second row of the beginning matrix has the multiplication symbol. The implied multiplication shown for 3y, 2z, 10y, and 3z in the second and third rows works, but it's not the best practice.

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"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

Regarding implied (or implicit) multiplication, I found this thread on the PTC Mathcad forums that indicates that the behavior is not always correct, which is why explicitly showing the multiplication is the best practice: https://community.ptc.com/t5/Mathcad/Prime-Bug-Imp...

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"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

Kind of annoying that the author didn't give a sheet to look at.

TTFN (ta ta for now)
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Hello all,
sorry for my late answer, many thanks for your help !