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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
asked | 1.2k views

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

rank = total number of variables
Hence, unique solution
answered by Boss (30.9k points)
selected
+1
Number of free variables=n-r=2-2=0, so no infinite, only unique solutions.
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
answered by Veteran (55.6k points)

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 :)

answered by Junior (911 points)

$2X2$  Minor with Determinant non - zero.

answered by Active (3.4k points)
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