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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

System of equations x + y = 2, 2x + 2y = 3 has ______ - Mathematics and Statistics

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प्रश्न

System of equations x + y = 2, 2x + 2y = 3 has ______

पर्याय

  • no solution

  • only one solution

  • many finite solutions.

  • infinite solutions.

MCQ
रिकाम्या जागा भरा
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उत्तर

no solution

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पाठ 1.2: Matrics - MCQ

संबंधित प्रश्‍न

If A = `[(2,-3,5),(3,2,-4),(1,1,-2)]` find A−1. Using A−1 solve the system of equations:

2x – 3y + 5z = 11

3x + 2y – 4z = –5

x + y – 2z = –3


Evaluate

\[\begin{vmatrix}2 & 3 & 7 \\ 13 & 17 & 5 \\ 15 & 20 & 12\end{vmatrix}^2 .\]


Evaluate
\[∆ = \begin{vmatrix}0 & \sin \alpha & - \cos \alpha \\ - \sin \alpha & 0 & \sin \beta \\ \cos \alpha & - \sin \beta & 0\end{vmatrix}\]


If \[A = \begin{bmatrix}2 & 5 \\ 2 & 1\end{bmatrix} \text{ and } B = \begin{bmatrix}4 & - 3 \\ 2 & 5\end{bmatrix}\] , verify that |AB| = |A| |B|.

 

Without expanding, show that the value of the following determinant is zero:

\[\begin{vmatrix}6 & - 3 & 2 \\ 2 & - 1 & 2 \\ - 10 & 5 & 2\end{vmatrix}\]


Without expanding, show that the value of the following determinant is zero:

\[\begin{vmatrix}1/a & a^2 & bc \\ 1/b & b^2 & ac \\ 1/c & c^2 & ab\end{vmatrix}\]


Without expanding, show that the value of the following determinant is zero:

\[\begin{vmatrix}\cos\left( x + y \right) & - \sin\left( x + y \right) & \cos2y \\ \sin x & \cos x & \sin y \\ - \cos x & \sin x & - \cos y\end{vmatrix}\]


Evaluate :

\[\begin{vmatrix}a & b + c & a^2 \\ b & c + a & b^2 \\ c & a + b & c^2\end{vmatrix}\]


Find values of k, if area of triangle is 4 square units whose vertices are 
(k, 0), (4, 0), (0, 2)


2x − y = 1
7x − 2y = −7


Prove that :

\[\begin{vmatrix}a + b + 2c & a & b \\ c & b + c + 2a & b \\ c & a & c + a + 2b\end{vmatrix} = 2 \left( a + b + c \right)^3\]

 


Prove that :

\[\begin{vmatrix}\left( b + c \right)^2 & a^2 & bc \\ \left( c + a \right)^2 & b^2 & ca \\ \left( a + b \right)^2 & c^2 & ab\end{vmatrix} = \left( a - b \right) \left( b - c \right) \left( c - a \right) \left( a + b + c \right) \left( a^2 + b^2 + c^2 \right)\]


3x + y = 19
3x − y = 23


3x + ay = 4
2x + ay = 2, a ≠ 0


x − 4y − z = 11
2x − 5y + 2z = 39
− 3x + 2y + z = 1


6x + y − 3z = 5
x + 3y − 2z = 5
2x + y + 4z = 8


xy = 5
y + z = 3
x + z = 4


5x − 7y + z = 11
6x − 8y − z = 15
3x + 2y − 6z = 7


3x + y = 5
− 6x − 2y = 9


An automobile company uses three types of steel S1S2 and S3 for producing three types of cars C1C2and C3. Steel requirements (in tons) for each type of cars are given below : 

  Cars
C1
C2 C3
Steel S1 2 3 4
S2 1 1 2
S3 3 2 1

Using Cramer's rule, find the number of cars of each type which can be produced using 29, 13 and 16 tons of steel of three types respectively.


If A = [aij] is a 3 × 3 scalar matrix such that a11 = 2, then write the value of |A|.

 

Write the value of the determinant \[\begin{vmatrix}2 & - 3 & 5 \\ 4 & - 6 & 10 \\ 6 & - 9 & 15\end{vmatrix} .\]


For what value of x is the matrix  \[\begin{bmatrix}6 - x & 4 \\ 3 - x & 1\end{bmatrix}\]  singular?


If \[A = \begin{bmatrix}\cos\theta & \sin\theta \\ - \sin\theta & \cos\theta\end{bmatrix}\] , then for any natural number, find the value of Det(An).


The number of distinct real roots of \[\begin{vmatrix}cosec x & \sec x & \sec x \\ \sec x & cosec x & \sec x \\ \sec x & \sec x & cosec x\end{vmatrix} = 0\]  lies in the interval
\[- \frac{\pi}{4} \leq x \leq \frac{\pi}{4}\]


Solve the following system of equations by matrix method:
3x + y = 7
5x + 3y = 12


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


Solve the following system of equations by matrix method:
 2x + 6y = 2
3x − z = −8
2x − y + z = −3


Show that the following systems of linear equations is consistent and also find their solutions:
2x + 3y = 5
6x + 9y = 15


Show that the following systems of linear equations is consistent and also find their solutions:
x + y + z = 6
x + 2y + 3z = 14
x + 4y + 7z = 30


Show that each one of the following systems of linear equation is inconsistent:
2x + 3y = 5
6x + 9y = 10


Show that each one of the following systems of linear equation is inconsistent:
4x − 2y = 3
6x − 3y = 5


Use product \[\begin{bmatrix}1 & - 1 & 2 \\ 0 & 2 & - 3 \\ 3 & - 2 & 4\end{bmatrix}\begin{bmatrix}- 2 & 0 & 1 \\ 9 & 2 & - 3 \\ 6 & 1 & - 2\end{bmatrix}\]  to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3.


A company produces three products every day. Their production on a certain day is 45 tons. It is found that the production of third product exceeds the production of first product by 8 tons while the total production of first and third product is twice the production of second product. Determine the production level of each product using matrix method.


2x − y + z = 0
3x + 2y − z = 0
x + 4y + 3z = 0


x + y + z = 0
x − y − 5z = 0
x + 2y + 4z = 0


Solve the following for x and y: \[\begin{bmatrix}3 & - 4 \\ 9 & 2\end{bmatrix}\binom{x}{y} = \binom{10}{ 2}\]


The system of equation x + y + z = 2, 3x − y + 2z = 6 and 3x + y + z = −18 has


Let \[X = \begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}, A = \begin{bmatrix}1 & - 1 & 2 \\ 2 & 0 & 1 \\ 3 & 2 & 1\end{bmatrix}\text{ and }B = \begin{bmatrix}3 \\ 1 \\ 4\end{bmatrix}\] . If AX = B, then X is equal to

 


Show that  \[\begin{vmatrix}y + z & x & y \\ z + x & z & x \\ x + y & y & z\end{vmatrix} = \left( x + y + z \right) \left( x - z \right)^2\]

 

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2x + y – z = 7

x – 3y + 2z = 1

x + 4y + δz = k, where δ, k ∈ R has infinitely many solutions, then δ + k is equal to ______.


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