Here we try to provided the 3D version of scatter plot.

Clear[cond, reg, pts];
SeedRandom[3];
cond = Resolve[
   Exists[t, x^2 + y^3 + z^2 + t^2 <= 1 && x + y - z == t^2], Reals];
reg = ImplicitRegion[cond, {x, y, z}];
pts = RandomPoint[
   RegionIntersection[reg, Cuboid[-10 {1, 1, 1}, 10 {1, 1, 1}]], 50];
ListPointPlot3D[{pts, 
  TranslationTransform[{0, 0, -10}]@ScalingTransform[{1, 1, 0}]@pts, 
  TranslationTransform[{0, -10, 0}]@ScalingTransform[{1, 0, 1}]@pts, 
  TranslationTransform[{-10, 0, 0}]@ScalingTransform[{0, 1, 1}]@pts}, 
 ViewPoint -> {5, 4, 3}, BoxRatios -> 1, AxesLabel -> {"X", "Y", "Z"},
  PlotStyle -> {Directive[AbsolutePointSize[Large], Blue], 
   Darker@Green, Darker@Yellow, Darker@Red}, 
 AxesEdge -> {{1, -1}, {1, -1}, {1, -1}}, 
 Boxed -> {Front, Bottom, Left}, 
 FaceGrids -> {{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}}, 
 PlotRangePadding -> None]

Here we try to provide the 3D version of scatter plot.

Clear[cond, reg, pts];
SeedRandom[3];
cond = Resolve[
   Exists[t, x^2 + y^3 + z^2 + t^2 <= 1 && x + y - z == t^2], Reals];
reg = ImplicitRegion[cond, {x, y, z}];
pts = RandomPoint[
   RegionIntersection[reg, Cuboid[-10 {1, 1, 1}, 10 {1, 1, 1}]], 50];
ListPointPlot3D[{pts, 
  TranslationTransform[{0, 0, -10}]@ScalingTransform[{1, 1, 0}]@pts, 
  TranslationTransform[{0, -10, 0}]@ScalingTransform[{1, 0, 1}]@pts, 
  TranslationTransform[{-10, 0, 0}]@ScalingTransform[{0, 1, 1}]@pts}, 
 ViewPoint -> {5, 4, 3}, BoxRatios -> 1, AxesLabel -> {"X", "Y", "Z"},
  PlotStyle -> {Directive[AbsolutePointSize[Large], Blue], 
   Darker@Green, Darker@Yellow, Darker@Red}, 
 AxesEdge -> {{1, -1}, {1, -1}, {1, -1}}, 
 Boxed -> {Front, Bottom, Left}, 
 FaceGrids -> {{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}}, 
 PlotRangePadding -> None]