Graphical representation of consistency of solution of simultaneous linear equations

CRITERIA 1:
If a1/ a2 ≠b1/b2 then lines intersect at one unique point and this is called unique solution.

Criteria 2: If a1/a2 =b1/b2 =c1/c2 then lines are overlapping and there are infintiley many solutions.

Criteria 2

Criteria 3: If a1/a2 =b1/b2 ≠c1/c2 then lines are parallel and this is condition of no solution or inconsistency.

criteria 3

LIne 1

Line 2

Criteria 1 and solution

a1 = 2 (slider from -10 to 20, step 1)
a2 = 1 (slider from -10 to 20, step 1)
b1 = 2 (slider from -10 to 20, step 1)
b2 = 0 (slider from -10 to 20, step 1)
c1 = 5 (slider from -10 to 20, step 1)
c2 = 1 (slider from -10 to 20, step 1)
eq1: (a1 * x) + (b1 * y) = c1
eq2: (a2 * x) + (b2 * y) = c2
text2: "a1 /a2 = " + a1 + "/" + a2 + ""
text3: "b1/ b2 = " + b1 + "/" + b2 + ""
text4: "c1 /c2 = " + c1 + "/" + c2 + ""
A = Intersect(eq2, eq1)
b = true
c = true
d = true
e = true
a = true