The way I understand the question, you would like to visualize the plane given
by each of the equations, and see whether they have a common intersection.

Here is one way to do that.

Define the three equations:

```
sage: x, y, z = SR.var('x y z')
sage: a, b, c = [2*x + 3*y - z == 15, x - 3*y + 3*z == -4, 4*x - 3*y - z == 19]
```

and the range of x, y, z where you want to plot:

```
sage: xx = (x, -10, 10)
sage: yy = (y, -10, 10)
sage: zz = (z, -10, 10)
```

Define the plots of the three planes, with different colors:

```
sage: pa = implicit_plot3d(a, xx, yy, zz, color='blue', alpha=0.3)
sage: pb = implicit_plot3d(b, xx, yy, zz, color='red', alpha=0.3)
sage: pc = implicit_plot3d(c, xx, yy, zz, color='green', alpha=0.3)
sage: p = a + b + c
```

Then you can show the combined plot using various viewers:

```
sage: p.show(aspect_ratio=1, viewer='jmol')
Launched jmol viewer for Graphics3d Object
sage: p.show(aspect_ratio=1, viewer='threejs')
Launched html viewer for Graphics3d Object
sage: p.show(aspect_ratio=1, viewer='tachyon')
Launched png viewer for Graphics3d Object
```

It seems that the threejs viewer does not take into account
the opacity setting given by the alpha option.

In the "SageNB" notebook you have an extra viewer available:

```
sage: p.show(aspect_ratio=1, viewer='canvas3d')
Launched png viewer for Graphics3d Object
```

sage: HyperplaneArrangements?