4x + 4y - 3z = 1
-8x + 6y -- 2z = 2
4x + 10y - 5z = – 13

2x+3y+3z=16. ( a

5x+4y+2z=13. (b

subtract

-3x -y +z = 3 (d = a-b

4x-y-pz=6 (c

7x -(1+p)z =3 (e =c-d

eliminate y from first two equations

7x-6z=-25 (f = 3b-4a

subtract

(5-p) z =- 22 (g= f-e

Answer p=5 makes (g) a contradiction

note

equations a and b each define a plane combining the two gives a straight line.

the choice of p=5 defines the plane c such that it is parallel to the line ab

hence the line(ab) and plane (c) do not intersect

what statement? is there an image?

h * s * a

h = history teacher

s = science teacher

a =   art teacher.

i see no data table, but just multiply the number of history teachers, science teachers, and art teachers.