Solution of Linear Equation in 2 Variables

Q. Question 1
The linear equation 2x - 5y = 7 has:

A) A unique solution
B) Two solution
C) Infinitely many solutions
D) No solution

Q. Question 6
Write whether the following statement is True or False?​​​​​​​
Every point on the graph of a linear equation in two variables does not represent a solution of the linear equation.

Q. Question 4
Plot the following points and check whether they are collinear or not.
(i) (1, 3), (-1, -1), (-2, -3)
(ii) (1, 1), (2, -3), (-1, -2)
(iii) (0, 0), (2, 2), (5, 5)

Q. 2y= -1/2. Solve the equation

Q. There are 3 groups of people, A, B, and C. The total wages of 6 people from A, 5 from group B, and 14 from group C is $\$$660. The wages of the 6 people from A are equal to that of the 10 people from B. Also, the wages of the 5 people from B are equal to that of the 10 people from C. Find the total wages of 20 people from group A, 15 from group B, and 20 from group C.

1. $1, 890
2. $2, 000
3. $1, 900
4. $1, 325

Q. Write the solution of the pair of linear equations $3x+4y=0$ and $2x-y=0$

Q. Write the solution of the pair of linear equations $4x+2y=5$ and $x-2y=0$.

Q.

Q. The option which is not a solution of the equation $2x+3y=6$, is

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

Q. Rob is working on a project to build a model house. Depending on the area of the base, he has to figure out the amount of material he will need. The given graph shows data from his previous attempts.


If he wants to build a house with a base area of 10 square meters, then how much material would Rob need?

1. $25kg$
2. $15kg$
3. $20kg$
4. $30kg$

Q. Which option is correct about the data representing linear and non-linear graphs?

Data 1

$x$	$2$	$4$	$6$
$y$	$3$	$6$	$9$

Data 2

$x$	$2$	$6$	$4$
$y$	$5$	$1$	$13$

1. Data 1: Non-linear relationship, and Data 2: Linear relationship
2. Data 1: Linear relationship, and Data 2: Linear relationship
3. Data 1: Non-linear relationship, and Data 2: Non-linear relationship
4. Data 1: Linear relationship, and Data 2: Non-linear relationship

Q. Draw the graph of the linear equation $x+y=7$ Verify from the graph that $(8,-1)$ is a solution of the given equation.

Q. A machine takes 2litres of petrol to start and then 3 litres per hour while running.If the equation thus formed is of the form of ax+by+c=0 .What is the value of $a$ when linear equation is written as $ax+by+c=0$

1. $2$
2. $0$
3. $3$
4. $1$

Q. Paul and Mathew are earning in the ratio of 3 : 4, and Mathew and Linda are earning in the ratio of 7 : m. If Linda earns $100 more than Mathew and $198 more than Paul, then what is the value of m?

1. $7$
2. $\frac{107}{56}$
3. $9$
4. $\frac{111}{14}$

Q. One red, two blue, and three green balls together weigh 20 pounds. Two red, four blue, and seven green balls together weigh 50 pounds. What is the weight of the green balls?

1. 8 pounds
2. 12 pounds
3. 9 pounds
4. 10 pounds