Question

What is value of a the following a linear equation infinity many solution 2x+ay=8:ax+8y=a

Answer 1

The value of a is 4.

Answer 2

Concept

For infinite many solutions the lines should be coincident. If two lines are coincident then there is no intercept diffrence between them.

GIven

1)  2x + ay = 8

2) ax + 8y = a

Find

Value of a

Solution

For infinite many solutions

a₁ / a₂ = b₁ / b₂ = c₁ / c₂

2x + ay = 8

Here

a₁= 2

b₁ = a

c₁ = 8

ax + 8y = a

Here a₂ = a b₂ =8 c₂ = a

Using Formula

2/a = a / 8 = 8/a

2/a = a/8

a² = 16

a = ±4

The value of a is ±4.

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