Solutions of a Linear Equation in Two Variables

Q.

Which of the following pair is a solution of the equation 2x - 3y = 7

1. (2, -3)

2. (5, 1)

3. (1, 5)

4. (0, 2)

Q. The coordinates of the point at which the equation 2x + 3y = 6 intersects the X-axis is

1. (0, 3)
2. (2, 3)
3. (2, 0)
4. (3, 0)

Q. Question 5
For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution. Justify whether it is true or false.

Q.

Determine the point on the graph of the linear equation 2x+5y=19 whose ordinate is 1½ times of its abscissa

Q.

Find the X and Y intercepts of 3x + 5y = 15

Q. If the temperature of a liquid can be measured in kelvin units as $x$ K or in fahrenheit units as $y^{\circ }$ F, the relation between the two systems of measurement of temperature is given by the linear equation.
$y=\frac{9}{5}(x-273)+32$

Find the temperature of the liquid in Fahrenheit, if the temperature of the liquid is 313 K.

1. 72
2. 96
3. 429
4. 104

Q.

Find the point on 5x - 3y = 4 where the ordinate is equal to the abscissa

Q. If a point $(1,2)$ lies on the line represented by the equation $3y=ax+7,$ then the value of $a$ is .

1. $-1$

2. $1$
3. $2$

Q. Which of the following lines passes through the origin?

1. $y=x+3$
2. $x=1$
3. $y=x$
4. $x=2y+4$

Q.

Find the value of $k$, when $a=-1$ and $b=4$ is the solution of the equation $-2a=-5b+k$.

1. 22
2. -18
3. 34
4. 20

Q.

Solutions of the equation 2x + 5y = 0 is:

1. 3, 0

2. 0, 0

3. 0, 4

4. -3, 2

Q.

Which of following is a solution of the equation, $2x+3y=11?$

1. $x=-2,y=-5$

2. $x=0,y=5$

3. $x=1,y=3$

4. $x=9,y=1$

Q. What is the value of 𝑘, if 𝑥 = 2 and 𝑦 =1 is a solution of the equation 2𝑥 + 3𝑦 = 𝑘? [2 marks]

Q.

The co-ordinate of point A in number line is 5.Find the co-ordinate of points on the same number line which are 13 units away from point A

Q. How many solutions does the equation 2x + 5y = 7 have?
($x$ and $y$ are natural numbers)

1. 0
2. 1
3. 2
4. Infinite

Q. Write four solutions for each of the following equations:
$\left(i\right)2x+y=9$
$\left(ii\right)xy+y=9$
$\left(iii\right)x=4y$

Q.

Which of these lines do not pass through the point (2, 2)?

1. y = 3x - 4

2. 2x = y - 6

3. y = 4 - x

4. 3y - 2x = 2

Q. If the temperature is $158F$, then find the temperature in Kelvin.

1. $150$
2. $473$
3. $273$
4. None of these

Q.

Identify the solutions for the given equation 4x+y=16?

1. (0, 16) & (4, 0)

2. (7, 4) & (0, 2)

3. (0, 8) & (8, 0)

4. (5, 0) & (3, 2)

Q.

Two solutions of this equation 2x + y = 1 are.

1. (2, 3) and (4, 5)

2. (0, 1) and (1, 0)

3. (0, 1) and ( ¹/₂ , 0)

4. (2, 0) and (1, 2)

Q. Which of the following is true regarding the solution of a linear equation if we multiply or divide both sides of the equation with a non-zero number?

1. It only changes in the case of multiplication
2. It changes
3. It only changes in the case of division
4. It remains the same

Q. The point $(5,8)$ satisfies the equation $4x-y=k$ the find the value of k

1. $5$
2. $8$
3. $12$
4. $15$

Q.

$6x+5y=9,$ cuts the X - axis on which point?

1. (0, )

2. (1, )

3. (2, 3)

4. ( , 0)

Q. If $kx-2ky+15=0$ passes through the point $(3,-1)$, then what is the value of $k$?

1. 1
2. 2
3. -3
4. 3

Q. A linear equation in two variables has solutions.

1. infinite
2. two
3. less than 4

Q. The point $(3,15)$ passes through the line represented by the equation .

1. $y=5x$
2. $y=4x$
3. $y=6x$

Q. x = 5 and y = 2 is a solution of the linear equation ___.

1. $x+2y=7$
2. $5x+2y=7$
3. $x+y=7$
4. $5x+2y=7$

Q. If the temperature of a liquid can be measured in Kelvin units as $xK$ or
in Fahrenheit units as $yF$, the relation between the two systems of
measurement of temperature is given by the linear equation

1. $33$
2. $104$
3. $76$
4. $21$

Q. Which value of k gives the solution x = 10 and y = 5 for the linear equation x = 4y - 2k ?

1. 11
2. -4
3. -2
4. 5

Q. Draw the graphs of the equation $3x+4y=7$ and $3x-2y=1$ and find their point of intersection of lines representing the equation.