a_1=

b_1=

c_1=

a_2=

b_2=

c_2=

INTERSECTING LINES - UNIQUE SOLUTION

COINCIDENT LINES- INFINITELY MANY SOLUTIONS

PARALLEL LINES - NO SOLUTION

Show Solution

CONDITIONS FOR CONSISTENCY OF PAIR OF LINEAR EQUATIONS

Let us consider two linear equations
a1x + b1y + c1 = 0 and
a2x + b2y + c2 = 0

Example 1:
2x + 3y -1 = 0
3x + 4y - 2 = 0

Example 2:
2x + 3y -1 = 0
4x + 6y -2 = 0

Example 3:
3x + 2y + 8 = 0
9x + 6 y + 5 = 0

EXAMPLES

Shivani Padmaja
CC BY SA

a1 = 11 (slider from -5 to 14, step 1)
b1 = 4 (slider from -2 to 8, step 1)
c1 = -1 (slider from -5 to 10, step 1)
InputBox1 = Textfield(a1)
InputBox2 = Textfield(b1)
InputBox3 = Textfield(c1)
eq1: (a1 * x) + (b1 * y) + c1 = 0
a2 = 8 (slider from -2 to 14, step 1)
b2 = 6 (slider from -2 to 8, step 1)
c2 = -2 (slider from -5 to 10, step 1)
InputBox4 = Textfield(a2)
InputBox5 = Textfield(b2)
InputBox6 = Textfield(c2)
eq2: (a2 * x) + (b2 * y) + c2 = 0
a = false
text1: "FOR UNIQUE SOLUTION
a1/a2 ≠ b1/b2  
i.e.  " + a1 + "/" + a2 + "≠" + b1 + "/" + b2 + ""
text2: "FOR INFINITELY MANY SOLUTIONS
a1/a2 = b1/b2 = c1/c2
i.e. " + a1 + "/" + a2 + " = " + b1 + "/" + b2 + " = " + c1 + "/" + c2 + ""
b = false
text3: "FOR NO SOLUTIONS
a1/a2 = b1/b2 ≠ c1/c2
i.e. " + a1 + "/" + a2 + " = " + b1 + "/" + b2 + " ≠ " + c1 + "/" + c2 + ""
c = false
A = Intersect(eq1, eq2)
text4: "Solution is " + A + ""
d = false
e = false