Solution of a LE in 2 variables

Q.

A pair of linear equations which has a unique solution $x=2,y=-3$ is

1. x + y = -1 ; 2x - 3y = -5

2. 2x - y = 1 ; 3x + 2y = 0

3. 2x + 5y = -11 ; 4x + 10y = -22

4. x - 4y -14 = 0 ; 5x - y - 13 = 0

Q.

Which of the following lines pass through the point (3, -2)?

1. All of the above.

2. $2x+3y=0$

3. $x+y=1$

4. $x-2y=7$

Q.

The point $\left(0,3\right)$ lies on the graph of the linear equation $3x+4y=12.$ Write whether the following statement is true or false . Justify your answer.

Q.

If the ordinate is twice the abscissa, then find the point where
$7x-3y=8.$

1. (8, 16)

2. (2, 4)

3. (3, 6)

4. (6, 3)

Q.

Find the value of k, if (1, 3k) lies on the line represented by the equation $kx+4y=26$.

1. 1

2. 0

3. 4

4. 2

Q.

Any point on the line represented by $x-2y=0$ can be written as $(2a,a)$.

1. True

2. False

Q.

If (a, 0) is a point on the line represented by the equation $2x-3y=4,$, find the value of a.

1. 1

2. 2

3. 0

4. -1

Q.

If (1, 3k) lies on $kx+4y=26,$ the value of $k$ is

___

Q.

Verify if (3, 2) is a solution of $3x-2y=4$.

1. True

2. False

Q.

Formulate the following problems as a pair of equations, and hence find their solutions:

Roohi travels $300km$ to her home partly by train and partly by bus. She takes $4$ hours if she travels $60km$ by train and the remaining by bus. If she travels $100km$ by train and the remaining by bus, she takes $10$ minutes longer. Find the speed of the train and the bus separately.

Q.

Which of the following lines passes through the origin?

1. 3x+5y = 0

2. x= 5

3. y = 3

4. x+y = 3

Q.

Which of these points lie on the line $7x+8y=61$?

1. (3, 4)

2. (2, 5)

3. (-3, 7)

4. (3, 5)

Q.

$x-y=0$ is a line which is

1. passing through origin

2. parallel to x-axis

3. parallel to y-axis

4. passing through (1, -1)

Q.

If (2, 2) lies on $4x+5y=k$, the value of $k$ is

___

Q.

Which among the following doesn’t have (-1, 3) as a solution?

1. 5x+3y-9=0

2. None of these

3. x+2y=5

4. x-2y+7= 0

Q.

Find the value of $k$, if (2, 3) lies on the line represented by the equation $2x=3y-k.$

1. 0

2. 2

3. 5

4. 3

Q.

Find the smallest value of $a$ and $b$ such that $3a=2b?$

1. a=1, b=1

2. a=2, b=3

3. a=2, b=2

4. a=3, b=2

Q.

Which among the following is the solution of $3x+4y=6?$

1. (-4, 5)

2. (3, 2)

3. (-2, 3)

4. (4, 3)

Q.

Which of the following equations does not pass through point (3, 3)

1. x-y=0

2. 2x-y=6

3. 3x+y = 12

4. 4x-2y-6=0

Q.

The line represented by the equation $3x-3y=6$ passes through the origin.

1. True

2. False

Q.

The line represented by the equation $3x-y=7$ passes through the point (3, 2).

1. False

2. True