Sarthaks Test
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Solve each of the following systems of homogeneous linear equations :

x + y – 2z = 0 

2x + y – 3z = 0 

5x + 4y – 9z = 0

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Best answer

Given Equations :

x + y – 2z = 0 

2x + y – 3z = 0 

5x + 4y – 9z = 0

Any system of equation can be written in matrix form as AX = B 

Now finding the Determinant of these set of equations,

= 1(1×(– 9) – 4×(– 3)) – 1(2×(– 9) – 5×(– 3)) – 2(4×2 – 5×1) 

= 1(– 9 + 12) – 1(– 18 + 15) – 2(8 – 5) 

= 1×3 –1 × (– 3) – 2×3 = 3 + 3 – 6 = 0 

Since,

D = 0 

so the system of equation has infinite solution. 

Now, 

let z = k 

⇒ x + y = 2k 

And,

2x + y = 3k 

Now, 

using the cramer’s rule

Hence, 

x = y = z = k.

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