Question

find the value of s for the following system of equation has infinitely many solution 2x -3y=7 ; (s+2) x - (2s+1) y=3(2s-1)​

Answer 1

Answer:

MATHS

MEDIUM

Show that the following system of linear equations is consistent and also find their solution:

x+y+z=6

x+2y+3z=14

x+4y+7z=30

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ANSWER

Given set of equations,

x+y+z=6

x+2y+3z=14

x+4y+7z=30

Arranging the above equations in form of matrix and finding the coefficient of matrix, we get,

A=

⎣

⎢

⎢

⎡

1

1

1

1

2

4

1

3

7

⎦

⎥

⎥

⎤

∣A∣=

∣

∣

∣

∣

∣

∣

∣

∣

1

1

1

1

2

4

1

3

7

∣

∣

∣

∣

∣

∣

∣

∣

=1(14−12)−1(7−3)+1(4−2)

∣A∣=0

det(A)=0. Therefore the system is consistent.

R

2

→R

2

−R

1

R

3

→R

3

−R

1

A∼

⎣

⎢

⎢

⎡

1

0

0

1

1

3

1

2

6

⎦

⎥

⎥

⎤

as, ρ(A)=2, submatrix is [

2

0

2

0

]

we get,

x+y+z=6

y+2z=8

Let z=k

y=8−2z=8−2k

x=6−y−z=6−8+2k−k=−2+k

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Answer 2

Question:-

Find the value of s for the following system of equation has infinitely many solution 2x -3y=7 ; (s+2) x - (2s+1) y=3(2s-1)

Solution:

$2x - 3y = 7 \\ \\ (s + 2)x - (2s + 1)y = 3(2s - 1)\\ \\ \frac{2}{s + 2} = \frac{3}{2s + 1} = \frac{7}{3(2s - 1)} \\ \\ \frac{2}{s + 2} = \frac{3}{2s + 1} \\ \\ 2(2s + 1) = 3(s + 2) \\ \\ 4s - 2 = 3s + 6 \\ \\ 4s - 3s = 6 - 2 \\ \\ s = 4$

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