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Homogeneous System of Equations

The number of...

Question

The number of solutions of the system equations $2 x + y - z = 7, x - 3 y + 3 z = 1, x + 4 y - 3 z = 5$ is

A

3

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B

2

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C

1

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D

0

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Solution

The correct option is B 1
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & - 1 1 & - 3 & 3 1 & 4 & - 3 \end{matrix} ∣ ∣ ∣ ∣$
$= - 6 + 6 - 7$
$Δ = - 7$
$∴ Δ \neq 0$
$∴$ trivial solution

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Similar questions

Q. The number of solutions of the system of equations:

2 x + y - z = 7

x - 3 y + 2 z = 1

x + 4 y - 3 z = 5

Q. The number of solutions of the triplet

(x, y, z)

in the following equations are

2 x + 4 y + 6 z = 8

x + 2 y + 3 z = 5

x + y + 3 z = 4

Q. The number of solutions of the system of equations:
2x + y − z = 7
x − 3y + 2z = 1
x + 4y − 3z = 5
(a) 3
(b) 2
(c) 1
(d) 0

Q. Solve the following system of equations, using matrix method;

x + 2 y + z = 7, x + 3 z = 11, 2 x - 3 y = 1

x + y + z

Q. Solve the following system of equations by matrix method:
(i) x + y − z = 3
2x + 3y + z = 10
3x − y − 7z = 1

(ii) x + y + z = 3
2x − y + z = − 1
2x + y − 3z = − 9

(iii) 6x − 12y + 25z = 4
4x + 15y − 20z = 3
2x + 18y + 15z = 10

(iv) 3x + 4y + 7z = 14
2x − y + 3z = 4
x + 2y − 3z = 0

(v)

\frac{2}{x} - \frac{3}{y} + \frac{3}{z} = 10 \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 10 \frac{3}{x} - \frac{1}{y} + \frac{2}{z} = 13

(vi) 5x + 3y + z = 16
2x + y + 3z = 19
x + 2y + 4z = 25

(vii) 3x + 4y + 2z = 8
2y − 3z = 3
x − 2y + 6z = −2

(viii) 2x + y + z = 2
x + 3y − z = 5
3x + y − 2z = 6

(ix) 2x + 6y = 2
3x − z = −8
2x − y + z = −3

(x) x − y + z = 2
2x − y = 0
2y − z = 1

(xi) 8x + 4y + 3z = 18
2x + y +z = 5
x + 2y + z = 5

(xii) x + y + z = 6
x + 2z = 7
3x + y + z = 12

(xiii)

\frac{2}{x} + \frac{3}{y} + \frac{10}{z} = 4, \frac{4}{x} - \frac{6}{y} + \frac{5}{z} = 1, \frac{6}{x} + \frac{9}{y} - \frac{20}{z} = 2; x, y, z \neq 0

(xiv) x − y + 2z = 7
3x + 4y − 5z = −5
2x − y + 3z = 12

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