1.6k views

How many solutions does the following system of linear equations have?

• $-x + 5y = -1$
• $x - y = 2$
• $x + 3y = 3$
1. infinitely many
2. two distinct solutions
3. unique
4. none
| 1.6k views

rank = r(A) = r(A|B) = 2

rank = total number of variables
Hence, unique solution
by Boss (30.5k points)
selected
+4
Number of free variables=n-r=2-2=0, so no infinite, only unique solutions.
0

I think for any set of linear non homogeneous equations two distinct solutions (option B) can never be possible..

C unique solution..
3 equation , 2 variable.
solve any two equation and check 3rd equation by putting values in 3rd equation.
x = 9/4 , y = 1/4
by Veteran (60k points)
0

@ sir, for given this type of equation i.e non-homogeneous eqn, how can I distinguish b/w infinitely many & no solution.

DIFFERENT APPROACH

all the equations are linearly independent. i.e non of the equations can be obtained by multiplying one of equation with a number (this means that no two vectors overlap each other leading to a rank of 3). therefore there will be a unique solution.

Correct me if wrong :)

by Junior (905 points)
0
how all equations are linearly independent.

multiplying -2 with eqn no. 2 & then add with eqn. no. 3 we'll get eqn no. 1

-2*(eqn2)+(eqn3) = (eqn1)

$2X2$  Minor with Determinant non - zero.

by Active (4.7k points)
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