diff --git a/lib/matplotlib/backend_bases.py b/lib/matplotlib/backend_bases.py
index fe8cc66913cc..29739b258b71 100644
--- a/lib/matplotlib/backend_bases.py
+++ b/lib/matplotlib/backend_bases.py
@@ -2755,10 +2755,15 @@ def show(self):
         warning in `.Figure.show`.
         """
         # This should be overridden in GUI backends.
-        if cbook._get_running_interactive_framework() != "headless":
-            raise NonGuiException(
-                f"Matplotlib is currently using {get_backend()}, which is "
-                f"a non-GUI backend, so cannot show the figure.")
+        if sys.platform == "linux" and not os.environ.get("DISPLAY"):
+            # We cannot check _get_running_interactive_framework() ==
+            # "headless" because that would also suppress the warning when
+            # $DISPLAY exists but is invalid, which is more likely an error and
+            # thus warrants a warning.
+            return
+        raise NonGuiException(
+            f"Matplotlib is currently using {get_backend()}, which is a "
+            f"non-GUI backend, so cannot show the figure.")
 
     def destroy(self):
         pass
diff --git a/lib/matplotlib/backends/backend_qt5.py b/lib/matplotlib/backends/backend_qt5.py
index 06a279fca24e..c25232f7942a 100644
--- a/lib/matplotlib/backends/backend_qt5.py
+++ b/lib/matplotlib/backends/backend_qt5.py
@@ -6,8 +6,7 @@
 import sys
 import traceback
 
-import matplotlib
-
+import matplotlib as mpl
 from matplotlib import backend_tools, cbook
 from matplotlib._pylab_helpers import Gcf
 from matplotlib.backend_bases import (
@@ -113,11 +112,8 @@ def _create_qApp():
                     is_x11_build = False
             else:
                 is_x11_build = hasattr(QtGui, "QX11Info")
-            if is_x11_build:
-                display = os.environ.get('DISPLAY')
-                if display is None or not re.search(r':\d', display):
-                    raise RuntimeError('Invalid DISPLAY variable')
-
+            if is_x11_build and not mpl._c_internal_utils.display_is_valid():
+                raise RuntimeError('Invalid DISPLAY variable')
             try:
                 QtWidgets.QApplication.setAttribute(
                     QtCore.Qt.AA_EnableHighDpiScaling)
@@ -574,7 +570,7 @@ def __init__(self, canvas, num):
 
         self.window.setCentralWidget(self.canvas)
 
-        if matplotlib.is_interactive():
+        if mpl.is_interactive():
             self.window.show()
             self.canvas.draw_idle()
 
@@ -601,9 +597,9 @@ def _widgetclosed(self):
     def _get_toolbar(self, canvas, parent):
         # must be inited after the window, drawingArea and figure
         # attrs are set
-        if matplotlib.rcParams['toolbar'] == 'toolbar2':
+        if mpl.rcParams['toolbar'] == 'toolbar2':
             toolbar = NavigationToolbar2QT(canvas, parent, True)
-        elif matplotlib.rcParams['toolbar'] == 'toolmanager':
+        elif mpl.rcParams['toolbar'] == 'toolmanager':
             toolbar = ToolbarQt(self.toolmanager, self.window)
         else:
             toolbar = None
@@ -619,7 +615,7 @@ def resize(self, width, height):
 
     def show(self):
         self.window.show()
-        if matplotlib.rcParams['figure.raise_window']:
+        if mpl.rcParams['figure.raise_window']:
             self.window.activateWindow()
             self.window.raise_()
 
@@ -792,8 +788,7 @@ def save_figure(self, *args):
         sorted_filetypes = sorted(filetypes.items())
         default_filetype = self.canvas.get_default_filetype()
 
-        startpath = os.path.expanduser(
-            matplotlib.rcParams['savefig.directory'])
+        startpath = os.path.expanduser(mpl.rcParams['savefig.directory'])
         start = os.path.join(startpath, self.canvas.get_default_filename())
         filters = []
         selectedFilter = None
@@ -811,8 +806,7 @@ def save_figure(self, *args):
         if fname:
             # Save dir for next time, unless empty str (i.e., use cwd).
             if startpath != "":
-                matplotlib.rcParams['savefig.directory'] = (
-                    os.path.dirname(fname))
+                mpl.rcParams['savefig.directory'] = os.path.dirname(fname)
             try:
                 self.canvas.figure.savefig(fname)
             except Exception as e:
diff --git a/lib/matplotlib/cbook/__init__.py b/lib/matplotlib/cbook/__init__.py
index f7dfa4c02b50..be12ac52407d 100644
--- a/lib/matplotlib/cbook/__init__.py
+++ b/lib/matplotlib/cbook/__init__.py
@@ -73,7 +73,7 @@ def _get_running_interactive_framework():
     if 'matplotlib.backends._macosx' in sys.modules:
         if sys.modules["matplotlib.backends._macosx"].event_loop_is_running():
             return "macosx"
-    if sys.platform.startswith("linux") and not os.environ.get("DISPLAY"):
+    if not _c_internal_utils.display_is_valid():
         return "headless"
     return None
 
diff --git a/setupext.py b/setupext.py
index a8a0ae7cdde7..0742230844fc 100644
--- a/setupext.py
+++ b/setupext.py
@@ -349,8 +349,10 @@ def get_extensions(self):
         # c_internal_utils
         ext = Extension(
             "matplotlib._c_internal_utils", ["src/_c_internal_utils.c"],
-            libraries=({"win32": ["ole32", "shell32", "user32"]}
-                       .get(sys.platform, [])))
+            libraries=({
+                "linux": ["dl"],
+                "win32": ["ole32", "shell32", "user32"],
+            }.get(sys.platform, [])))
         yield ext
         # contour
         ext = Extension(
diff --git a/src/_c_internal_utils.c b/src/_c_internal_utils.c
index caca31585019..4a61fe5b6ee7 100644
--- a/src/_c_internal_utils.c
+++ b/src/_c_internal_utils.c
@@ -1,12 +1,68 @@
 #define PY_SSIZE_T_CLEAN
 #include <Python.h>
+#ifdef __linux__
+#include <dlfcn.h>
+#endif
 #ifdef _WIN32
 #include <Objbase.h>
 #include <Shobjidl.h>
 #include <Windows.h>
 #endif
 
-static PyObject* mpl_GetCurrentProcessExplicitAppUserModelID(PyObject* module)
+static PyObject*
+mpl_display_is_valid(PyObject* module)
+{
+#ifdef __linux__
+    void* libX11;
+    // The getenv check is redundant but helps performance as it is much faster
+    // than dlopen().
+    if (getenv("DISPLAY")
+        && (libX11 = dlopen("libX11.so.6", RTLD_LAZY))) {
+        struct Display* display = NULL;
+        struct Display* (* XOpenDisplay)(char const*) =
+            dlsym(libX11, "XOpenDisplay");
+        int (* XCloseDisplay)(struct Display*) =
+            dlsym(libX11, "XCloseDisplay");
+        if (XOpenDisplay && XCloseDisplay
+                && (display = XOpenDisplay(NULL))) {
+            XCloseDisplay(display);
+        }
+        if (dlclose(libX11)) {
+            PyErr_SetString(PyExc_RuntimeError, dlerror());
+            return NULL;
+        }
+        if (display) {
+            Py_RETURN_TRUE;
+        }
+    }
+    void* libwayland_client;
+    if (getenv("WAYLAND_DISPLAY")
+        && (libwayland_client = dlopen("libwayland-client.so.0", RTLD_LAZY))) {
+        struct wl_display* display = NULL;
+        struct wl_display* (* wl_display_connect)(char const*) =
+            dlsym(libwayland_client, "wl_display_connect");
+        void (* wl_display_disconnect)(struct wl_display*) =
+            dlsym(libwayland_client, "wl_display_disconnect");
+        if (wl_display_connect && wl_display_disconnect
+                && (display = wl_display_connect(NULL))) {
+            wl_display_disconnect(display);
+        }
+        if (dlclose(libwayland_client)) {
+            PyErr_SetString(PyExc_RuntimeError, dlerror());
+            return NULL;
+        }
+        if (display) {
+            Py_RETURN_TRUE;
+        }
+    }
+    Py_RETURN_FALSE;
+#else
+    Py_RETURN_TRUE;
+#endif
+}
+
+static PyObject*
+mpl_GetCurrentProcessExplicitAppUserModelID(PyObject* module)
 {
 #ifdef _WIN32
     wchar_t* appid = NULL;
@@ -22,7 +78,8 @@ static PyObject* mpl_GetCurrentProcessExplicitAppUserModelID(PyObject* module)
 #endif
 }
 
-static PyObject* mpl_SetCurrentProcessExplicitAppUserModelID(PyObject* module, PyObject* arg)
+static PyObject*
+mpl_SetCurrentProcessExplicitAppUserModelID(PyObject* module, PyObject* arg)
 {
 #ifdef _WIN32
     wchar_t* appid = PyUnicode_AsWideCharString(arg, NULL);
@@ -40,7 +97,8 @@ static PyObject* mpl_SetCurrentProcessExplicitAppUserModelID(PyObject* module, P
 #endif
 }
 
-static PyObject* mpl_GetForegroundWindow(PyObject* module)
+static PyObject*
+mpl_GetForegroundWindow(PyObject* module)
 {
 #ifdef _WIN32
   return PyLong_FromVoidPtr(GetForegroundWindow());
@@ -49,7 +107,8 @@ static PyObject* mpl_GetForegroundWindow(PyObject* module)
 #endif
 }
 
-static PyObject* mpl_SetForegroundWindow(PyObject* module, PyObject *arg)
+static PyObject*
+mpl_SetForegroundWindow(PyObject* module, PyObject *arg)
 {
 #ifdef _WIN32
   HWND handle = PyLong_AsVoidPtr(arg);
@@ -66,6 +125,12 @@ static PyObject* mpl_SetForegroundWindow(PyObject* module, PyObject *arg)
 }
 
 static PyMethodDef functions[] = {
+    {"display_is_valid", (PyCFunction)mpl_display_is_valid, METH_NOARGS,
+     "display_is_valid()\n--\n\n"
+     "Check whether the current X11 or Wayland display is valid.\n\n"
+     "On Linux, returns True if either $DISPLAY is set and XOpenDisplay(NULL)\n"
+     "succeeds, or $WAYLAND_DISPLAY is set and wl_display_connect(NULL)\n"
+     "succeeds.  On other platforms, always returns True."},
     {"Win32_GetCurrentProcessExplicitAppUserModelID",
      (PyCFunction)mpl_GetCurrentProcessExplicitAppUserModelID, METH_NOARGS,
      "Win32_GetCurrentProcessExplicitAppUserModelID()\n--\n\n"
@@ -83,7 +148,7 @@ static PyMethodDef functions[] = {
      "always returns None."},
     {"Win32_SetForegroundWindow",
      (PyCFunction)mpl_SetForegroundWindow, METH_O,
-     "Win32_SetForegroundWindow(hwnd)\n--\n\n"
+     "Win32_SetForegroundWindow(hwnd, /)\n--\n\n"
      "Wrapper for Windows' SetForegroundWindow.  On non-Windows platforms, \n"
      "a no-op."},
     {NULL, NULL}};  // sentinel.