diff --git a/test/nonlinearsystem.jl b/test/nonlinearsystem.jl
index a71d34a880..c42eb6f87b 100644
--- a/test/nonlinearsystem.jl
+++ b/test/nonlinearsystem.jl
@@ -325,3 +325,17 @@ end
     prob = @test_nowarn NonlinearProblem(sys, nothing)
     @test_nowarn solve(prob)
 end
+
+@testset "System of linear equations with vector variable" begin
+    # 1st example in https://en.wikipedia.org/w/index.php?title=System_of_linear_equations&oldid=1247697953
+    @variables x[1:3]
+    A = [3 2 -1
+         2 -2 4
+         -1 1/2 -1]
+    b = [1, -2, 0]
+    @named sys = NonlinearSystem(A * x ~ b, [x], [])
+    sys = structural_simplify(sys)
+    prob = NonlinearProblem(sys, unknowns(sys) .=> 0.0)
+    sol = solve(prob)
+    @test all(sol[x] .≈ A \ b)
+end
diff --git a/test/reduction.jl b/test/reduction.jl
index 064a2efd81..80969d5794 100644
--- a/test/reduction.jl
+++ b/test/reduction.jl
@@ -178,6 +178,7 @@ A = reshape(1:(N^2), N, N)
 eqs = xs ~ A * xs
 @named sys′ = NonlinearSystem(eqs, [xs], [])
 sys = structural_simplify(sys′)
+@test length(equations(sys)) == 3 && length(observed(sys)) == 2
 
 # issue 958
 @parameters k₁ k₂ k₋₁ E₀