Question

Find the value of 'a' for which the system of equations ax + 2y - 4 = 0 and x - y - 3 = 0 will represent intersecting lines?

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Answer 1

Required Value of "a" ≠ – 2

Given Terms:

• Equations are ax + 2y – 4 = 0 and x – y – 3 = 0

Need To Find:

• Value of a for which system of equations will represent intersecting lines ?

Solution: For unique solution or intersecting lines the formula is

➠ a¹/a² ≠ b¹/b²

From the given equations we have

• a¹ = a
• b¹ = 2
• c¹ = – 4

• a² = 1
• b² = – 1
• c² = – 3

By equating these equations

➥ a/1 ≠ 2/–1

➥ a × – 1 ≠ 2 × 1

➥ – a ≠ 2

➥ a ≠ – 2

The given system of equations will have a unique solution or will represent intersecting lines for all the real values of "a" other than – 2.

Answer 2

Step-by-step explanation:

given a1/a2 ≠ b1/b2

a1 = a b1= 2 c1=-4

a2= 1 b2= -1 c2=-3

a/1≠2/-1

a× -1 ≠ 2× 1

-a ≠ 2

a≠ 2