Question

find the value of alpha and beta for which the pair of linear equations 2x+3y=7,2 alpha x+(alpha+beta)y=28 has infinite number of solution

Answer 1

Answer:

alpha is 4 and beta is 8

Step-by-step explanation:

a1/a2 = b1/b2 = c1/c2

a1=2, b1=3, c1=-7

a2=2alpha, b2=alpha+beta, c2=-28.

2/2alpha = 3/alpha+beta = 7/28

ai/a2=c1/c2

2/2alpha= 7/28

2.28= 7.(2+beta)

=4

b1/b2=c1/c2

3/4+beta=7/28

3.28=28+beta

beta=8

Answer 2

Concept:

A system of equations is a set of numbers and variables with mathematical operations.

Given:

2x + 3y = 7

And,

αx + ( α + β ) y = 28

Find:

We are asked to find the value of alpha and beta.

Solution:

We have,

2x + 3y = 7

And,

αx + ( α + β ) y = 28

And,

The pair of linear equations have infinite numbers of solutions,

Now,

For infinite number of solutions,

a₁/a₂ = b₁/b₂ = c₁/c₂

So,

From the given linear equations,

2/α = 3/( α + β ) = 7/28

So,

Let,

2/α =7/28

we get,

56 = 7α

i.e.

α = 8,

Now,

2/α = 3/( α + β )

i.e.

2/8 = 3/( 8 + β )

we get,

16 + 2β = 24

i.e.

2β = 8

So,

β = 4

Hence, the value of alpha and beta for which the pair of linear equations are 8 and 4.

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