You visited us 1 times! Enjoying our articles? Unlock Full Access!

System of Linear Equations

Number of sol...

Question

Number of solutions for the system of equations $x + 2 y + z = 0, 3 x + 5 y + 2 z = 2$ and $2 x + 4 y + 2 z = 1$

0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

infinity

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $0$
Consider the first equation
$x + 2 y + z = 0 \dots (1)$

Consider the last equation
$2 x + 4 y + 2 z = 1$
$\Rightarrow x + 2 y + z = \frac{1}{2} \dots (2)$

Hence both $(1)$ and $(2)$ consist of a system of parallel planes.
Therefore, they never intersect and hence they do not have any common solution.

Suggest Corrections

Similar questions

2 x + y - z = 7

x - 3 y + 2 z = 1

x + 4 y - 3 z = 5

λ

2 x + 4 y - λ z = 0

4 x + λ y + 2 z = 0, λ x + 2 y + 2 z = 0

x + 2 y - z = 7, 2 x - y + z = 2, 3 x - 5 y + 2 z = - 7

Number of solutions for the system of linear equations, will be,

x + y + z =6

x + 2y + 3z = 14

x + 4y + 2z =30

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program